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Reinhoffer C, Esser S, Esser S, Mashkovich EA, Germanskiy S, Gegenwart P, Anders F, van Loosdrecht PHM, Wang Z. Strong Terahertz Third-Harmonic Generation by Kinetic Heavy Quasiparticles in CaRuO_{3}. PHYSICAL REVIEW LETTERS 2024; 132:196501. [PMID: 38804953 DOI: 10.1103/physrevlett.132.196501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Accepted: 04/15/2024] [Indexed: 05/29/2024]
Abstract
We report on time-resolved nonlinear terahertz spectroscopy of a strongly correlated ruthenate, CaRuO_{3}, as a function of temperature, frequency, and terahertz field strength. Third-harmonic radiation for frequencies up to 2.1 THz is observed evidently at low temperatures below 80 K, where the low-frequency linear dynamical response deviates from the Drude model and a coherent heavy quasiparticle band emerges by strong correlations associated with the Hund's coupling. Phenomenologically, by taking an experimentally observed frequency-dependent scattering rate, the deviation of the field driven kinetics from the Drude behavior is reconciled in a time-dependent Boltzmann description, which allows an attribution of the observed third-harmonic generation to the terahertz field driven nonlinear kinetics of the heavy quasiparticles.
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Affiliation(s)
- Chris Reinhoffer
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany
| | - Sven Esser
- Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - Sebastian Esser
- Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | | | - Semyon Germanskiy
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany
| | - Philipp Gegenwart
- Experimental Physics VI, Center for Electronic Correlations and Magnetism, University of Augsburg, 86159 Augsburg, Germany
| | - Frithjof Anders
- Department of Physics, TU Dortmund University, 44227 Dortmund, Germany
| | | | - Zhe Wang
- Institute of Physics II, University of Cologne, 50937 Cologne, Germany
- Department of Physics, TU Dortmund University, 44227 Dortmund, Germany
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2
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Begg SE, Hanai R. Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity. PHYSICAL REVIEW LETTERS 2024; 132:120401. [PMID: 38579202 DOI: 10.1103/physrevlett.132.120401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Revised: 12/26/2023] [Accepted: 02/20/2024] [Indexed: 04/07/2024]
Abstract
We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.
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Affiliation(s)
- Samuel E Begg
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
| | - Ryo Hanai
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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3
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Zhang Y, Barthel T. Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2022; 129:120401. [PMID: 36179179 DOI: 10.1103/physrevlett.129.120401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in D>1 dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.
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Affiliation(s)
- Yikang Zhang
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Thomas Barthel
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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4
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Marino J. Universality Class of Ising Critical States with Long-Range Losses. PHYSICAL REVIEW LETTERS 2022; 129:050603. [PMID: 35960567 DOI: 10.1103/physrevlett.129.050603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2021] [Revised: 01/27/2022] [Accepted: 07/08/2022] [Indexed: 06/15/2023]
Abstract
We show that spatial resolved dissipation can act on d-dimensional spin systems in the Ising universality class by qualitatively modifying the nature of their critical points. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as ∝q^{α}, with α a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r^{(α+d)}. This yields a class of soft modes asymptotically decoupled from dissipation at small momenta, which are responsible for the emergence of a critical scaling regime ascribable to the nonunitary counterpart of the universality class of long-range interacting Ising models. For α<1 we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial (∼∂_{t}^{2}) and frictional (∼∂_{t}) kinetic coefficients, and driven by a gapless Markovian noise with variance ∝q^{α} at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Our Letter lays out perspectives for a revision of universality in driven open systems by employing dark states tailored by programmable dissipation.
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Affiliation(s)
- Jamir Marino
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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5
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Far-from-equilibrium universality in the two-dimensional Heisenberg model. Proc Natl Acad Sci U S A 2022; 119:e2122599119. [PMID: 35787047 PMCID: PMC9282433 DOI: 10.1073/pnas.2122599119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
We characterize the universal far-from-equilibrium dynamics of the two-dimensional quantum Heisenberg magnet isolated from its environment. For a broad range of initial conditions, we find a long-lived universal prethermal regime characterized by self-similar behavior of spin-spin correlations. We analytically derive the spatial-temporal scaling exponents and find excellent agreement with numerics using phase space methods. The scaling exponents are insensitive to the choice of initial conditions, which include coherent and incoherent spin states with values of total magnetization and energy in a wide range. Compared to previously studied self-similar dynamics in nonequilibrium O(n) field theories and Bose gases, we find qualitatively distinct scaling behavior originating from the presence of spin modes that remain gapless at long times and are protected by the global SU(2) symmetry. Our predictions, which suggest a distinct nonequilibrium universality class from Bose gases and O(n) theories, are readily testable in ultracold atoms simulators of Heisenberg magnets.
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6
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Renormalizing Open Quantum Field Theories. UNIVERSE 2022. [DOI: 10.3390/universe8020127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR and the UV particle modes. It is argued that the open interaction channels have to be taken into account in quantum field theory defined by the help of a cutoff, and a non-perturbative UV-IR entanglement is found in closed or almost closed models.
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7
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Kelly SP, Rey AM, Marino J. Effect of Active Photons on Dynamical Frustration in Cavity QED. PHYSICAL REVIEW LETTERS 2021; 126:133603. [PMID: 33861099 DOI: 10.1103/physrevlett.126.133603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 03/05/2021] [Indexed: 06/12/2023]
Abstract
We study the far-from-equilibrium dynamical regimes of a many-body spin-boson model with disordered couplings relevant for cavity QED and trapped ion experiments, using the discrete truncated Wigner approximation. We focus on the dynamics of spin observables upon varying the disorder strength and the frequency of the photons, finding that the latter can considerably alter the structure of the system's dynamical responses. When the photons evolve at a similar rate as the spins, they can induce qualitatively distinct frustrated dynamics characterized by either logarithmic or algebraically slow relaxation. The latter illustrates resilience of glassylike dynamics in the presence of active photonic degrees of freedom, suggesting that disordered quantum many-body systems with resonant photons or phonons can display a rich diagram of nonequilibrium responses, with near future applications for quantum information science.
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Affiliation(s)
- Shane P Kelly
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
| | - Ana Maria Rey
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Jamir Marino
- Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany
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8
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Lieu S, Belyansky R, Young JT, Lundgren R, Albert VV, Gorshkov AV. Symmetry Breaking and Error Correction in Open Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 125:240405. [PMID: 33412027 DOI: 10.1103/physrevlett.125.240405] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 11/10/2020] [Indexed: 06/12/2023]
Abstract
Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_{n} symmetry-breaking transitions for both cases. In the case of Z_{2}, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.
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Affiliation(s)
- Simon Lieu
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Ron Belyansky
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Jeremy T Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Rex Lundgren
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Victor V Albert
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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9
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Lundgren R, Gorshkov AV, Maghrebi MF. Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model. PHYSICAL REVIEW. A 2020; 102:10.1103/PhysRevA.102.032218. [PMID: 34136732 PMCID: PMC8204515 DOI: 10.1103/physreva.102.032218] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.
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Affiliation(s)
- Rex Lundgren
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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10
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Shirai T, Mori T. Thermalization in open many-body systems based on eigenstate thermalization hypothesis. Phys Rev E 2020; 101:042116. [PMID: 32422755 DOI: 10.1103/physreve.101.042116] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2019] [Accepted: 03/20/2020] [Indexed: 11/07/2022]
Abstract
We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that the system Hamiltonian obeys the eigenstate thermalization hypothesis (ETH) and the perturbation theory in the weak system-environment coupling is valid in the thermodynamic limit. We derive a criterion to guarantee the validity of the perturbation theory, which is satisfied in the thermodynamic limit for sufficiently weak dissipation when the Liouvillian is gapped for bulk-dissipated systems, while the perturbation theory breaks down in boundary-dissipated chaotic systems due to the presence of diffusive transports. We numerically confirm these theoretical predictions. This paper suggests a connection between steady states of macroscopic open quantum systems and the ETH.
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Affiliation(s)
- Tatsuhiko Shirai
- Green Computing Systems Research Organization, Waseda University, Tokyo 162-0042, Japan
| | - Takashi Mori
- RIKEN Center for Emergent Matter Science, Wako 351-0198, Japan
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11
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Young JT, Gorshkov AV, Foss-Feig M, Maghrebi MF. Nonequilibrium Fixed Points of Coupled Ising Models. PHYSICAL REVIEW. X 2020; 10:10.1103/physrevx.10.011039. [PMID: 33364075 PMCID: PMC7756198 DOI: 10.1103/physrevx.10.011039] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) ℤ 2 symmetry. However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a ℤ 2 × ℤ 2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.
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Affiliation(s)
- Jeremy T. Young
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Mohammad F. Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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12
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Berdanier W, Marino J, Altman E. Universal Dynamics of Stochastically Driven Quantum Impurities. PHYSICAL REVIEW LETTERS 2019; 123:230604. [PMID: 31868487 DOI: 10.1103/physrevlett.123.230604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 06/10/2023]
Abstract
We show that the dynamics of a quantum impurity subject to a stochastic drive on one side and coupled to a quantum critical system on the other display a universal behavior inherited from the quantum critical scaling. Using boundary conformal field theory, we formulate a generic ansatz for the dynamical scaling form of the typical Loschmidt echo and corroborate it with exact numerical calculations in the case of a spin impurity driven by shot noise in a quantum Ising chain. We find that due to rare events the dynamics of the mean echo can follow very different dynamical scaling than the typical echo for certain classes of drives. Our results are insensitive to irrelevant perturbations of the bulk critical model and apply to all the microscopic models in the same universality class.
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Affiliation(s)
- William Berdanier
- Department of Physics, University of California, Berkeley, California 94720, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - Jamir Marino
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Quantum Matter Physics, University of Geneva, 1211, Geneva, Switzerland
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, California 94720, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
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13
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Puel TO, Chesi S, Kirchner S, Ribeiro P. Mixed-Order Symmetry-Breaking Quantum Phase Transition Far from Equilibrium. PHYSICAL REVIEW LETTERS 2019; 122:235701. [PMID: 31298904 DOI: 10.1103/physrevlett.122.235701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2018] [Indexed: 06/10/2023]
Abstract
We study the current-carrying steady state of a transverse field Ising chain coupled to magnetic thermal reservoirs and obtain the nonequilibrium phase diagram as a function of the magnetization potential of the reservoirs. Upon increasing the magnetization bias we observe a discontinuous jump of the magnetic order parameter that coincides with a divergence of the correlation length. For steady states with a nonvanishing conductance, the entanglement entropy at zero temperature displays a bias dependent logarithmic correction that violates the area law and differs from the well-known equilibrium case. Our findings show that out-of-equilibrium conditions allow for novel critical phenomena not possible at equilibrium.
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Affiliation(s)
- T O Puel
- Beijing Computational Science Research Center, Beijing 100193, China
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- Zhejiang Province Key Laboratory of Quantum Technology and Devices, Zhejiang University, Hangzhou 310027, China
| | - Stefano Chesi
- Beijing Computational Science Research Center, Beijing 100193, China
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - S Kirchner
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
- Zhejiang Province Key Laboratory of Quantum Technology and Devices, Zhejiang University, Hangzhou 310027, China
| | - P Ribeiro
- Beijing Computational Science Research Center, Beijing 100193, China
- CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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14
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Balachandran V, Benenti G, Pereira E, Casati G, Poletti D. Perfect Diode in Quantum Spin Chains. PHYSICAL REVIEW LETTERS 2018; 120:200603. [PMID: 29864301 DOI: 10.1103/physrevlett.120.200603] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Revised: 02/07/2018] [Indexed: 06/08/2023]
Abstract
We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.
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Affiliation(s)
- Vinitha Balachandran
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Giuliano Benenti
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Milano, via Celoria 16, 20133 Milano, Italy
- NEST, Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - Emmanuel Pereira
- Departamento de Física-Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30.161-970 Belo Horizonte MG, Brazil
| | - Giulio Casati
- Center for Nonlinear and Complex Systems, Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy
- International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário-Lagoa Nova, Caixa Postale 1613, Natal, Rio Grande Do Norte 59078-970, Brazil
| | - Dario Poletti
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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15
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Lin YC, Yang PY, Zhang WM. Non-equilibrium quantum phase transition via entanglement decoherence dynamics. Sci Rep 2016; 6:34804. [PMID: 27713556 PMCID: PMC5054423 DOI: 10.1038/srep34804] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2016] [Accepted: 09/20/2016] [Indexed: 01/05/2023] Open
Abstract
We investigate the decoherence dynamics of continuous variable entanglement as the system-environment coupling strength varies from the weak-coupling to the strong-coupling regimes. Due to the existence of localized modes in the strong-coupling regime, the system cannot approach equilibrium with its environment, which induces a nonequilibrium quantum phase transition. We analytically solve the entanglement decoherence dynamics for an arbitrary spectral density. The nonequilibrium quantum phase transition is demonstrated as the system-environment coupling strength varies for all the Ohmic-type spectral densities. The 3-D entanglement quantum phase diagram is obtained.
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Affiliation(s)
- Yu-Chen Lin
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
| | - Pei-Yun Yang
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
| | - Wei-Min Zhang
- Department of Physics and Centre for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan
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16
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Sieberer LM, Buchhold M, Diehl S. Keldysh field theory for driven open quantum systems. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:096001. [PMID: 27482736 DOI: 10.1088/0034-4885/79/9/096001] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
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Affiliation(s)
- L M Sieberer
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
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17
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Marcuzzi M, Buchhold M, Diehl S, Lesanovsky I. Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations. PHYSICAL REVIEW LETTERS 2016; 116:245701. [PMID: 27367395 DOI: 10.1103/physrevlett.116.245701] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2016] [Indexed: 06/06/2023]
Abstract
Stochastic processes with absorbing states feature examples of nonequilibrium universal phenomena. While the classical regime has been thoroughly investigated in the past, relatively little is known about the behavior of these nonequilibrium systems in the presence of quantum fluctuations. Here, we theoretically address such a scenario in an open quantum spin model which, in its classical limit, undergoes a directed percolation phase transition. By mapping the problem to a nonequilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin flips alters the nature of the transition such that it becomes first order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in a low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.
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Affiliation(s)
- Matteo Marcuzzi
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Michael Buchhold
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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18
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Marino J, Diehl S. Driven Markovian Quantum Criticality. PHYSICAL REVIEW LETTERS 2016; 116:070407. [PMID: 26943517 DOI: 10.1103/physrevlett.116.070407] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Indexed: 06/05/2023]
Abstract
We identify a new universality class in one-dimensional driven open quantum systems with a dark state. Salient features are the persistence of both the microscopic nonequilibrium conditions as well as the quantum coherence of dynamics close to criticality. This provides a nonequilibrium analogue of quantum criticality, and is sharply distinct from more generic driven systems, where both effective thermalization as well as asymptotic decoherence ensue, paralleling classical dynamical criticality. We quantify universality by computing the full set of independent critical exponents within a functional renormalization group approach.
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Affiliation(s)
- Jamir Marino
- Institute of Theoretical Physics, TU Dresden, D-01062 Dresden, Germany
- Institute of Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
| | - Sebastian Diehl
- Institute of Theoretical Physics, TU Dresden, D-01062 Dresden, Germany
- Institute of Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
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19
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Maghrebi MF, Gorshkov AV. Nonequilibrium many-body steady states via Keldysh formalism. PHYSICAL REVIEW. B 2016; 93:10.1103/PhysRevB.93.014307. [PMID: 31093593 PMCID: PMC6513009 DOI: 10.1103/physrevb.93.014307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
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Affiliation(s)
- Mohammad F. Maghrebi
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V. Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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20
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Ribeiro P, Zamani F, Kirchner S. Steady-State Dynamics and Effective Temperature for a Model of Quantum Criticality in an Open System. PHYSICAL REVIEW LETTERS 2015; 115:220602. [PMID: 26650286 DOI: 10.1103/physrevlett.115.220602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2015] [Indexed: 06/05/2023]
Abstract
We study the thermal and nonthermal steady-state scaling functions and the steady-state dynamics of a model of local quantum criticality. The model we consider, i.e., the pseudogap Kondo model, allows us to study the concept of effective temperatures near fully interacting as well as weak-coupling fixed points. In the vicinity of each fixed point we establish the existence of an effective temperature-different at each fixed point-such that the equilibrium fluctuation-dissipation theorem is recovered. Most notably, steady-state scaling functions in terms of the effective temperatures coincide with the equilibrium scaling functions. This result extends to higher correlation functions as is explicitly demonstrated for the Kondo singlet strength. The nonlinear charge transport is also studied and analyzed in terms of the effective temperature.
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Affiliation(s)
- P Ribeiro
- Russian Quantum Center, Novaya street 100 A, Skolkovo, Moscow area, 143025 Russia and CeFEMA, Instituto Superior Técnico, Universidade de Lisboa Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
| | - F Zamani
- Max Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany and Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - S Kirchner
- Center for Correlated Matter, Zhejiang University, Hangzhou, Zhejiang 310058, China
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21
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Real-time observation of fluctuations at the driven-dissipative Dicke phase transition. Proc Natl Acad Sci U S A 2013; 110:11763-7. [PMID: 23818599 DOI: 10.1073/pnas.1306993110] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We experimentally study the influence of dissipation on the driven Dicke quantum phase transition, realized by coupling external degrees of freedom of a Bose-Einstein condensate to the light field of a high-finesse optical cavity. The cavity provides a natural dissipation channel, which gives rise to vacuum-induced fluctuations and allows us to observe density fluctuations of the gas in real-time. We monitor the divergence of these fluctuations over two orders of magnitude while approaching the phase transition, and observe a behavior that deviates significantly from that expected for a closed system. A correlation analysis of the fluctuations reveals the diverging time scale of the atomic dynamics and allows us to extract a damping rate for the external degree of freedom of the atoms. We find good agreement with our theoretical model including dissipation via both the cavity field and the atomic field. Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.
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22
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Sieberer LM, Huber SD, Altman E, Diehl S. Dynamical critical phenomena in driven-dissipative systems. PHYSICAL REVIEW LETTERS 2013; 110:195301. [PMID: 23705715 DOI: 10.1103/physrevlett.110.195301] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2013] [Revised: 03/28/2013] [Indexed: 06/02/2023]
Abstract
We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.
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Affiliation(s)
- L M Sieberer
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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23
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Tsuji N, Eckstein M, Werner P. Nonthermal antiferromagnetic order and nonequilibrium criticality in the Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:136404. [PMID: 23581350 DOI: 10.1103/physrevlett.110.136404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2012] [Revised: 01/25/2013] [Indexed: 05/23/2023]
Abstract
We study dynamical phase transitions from antiferromagnetic to paramagnetic states driven by an interaction quench in the fermionic Hubbard model using the nonequilibrium dynamical mean-field theory. We identify two dynamical transition points where the relaxation behavior qualitatively changes: one corresponds to the thermal phase transition at which the order parameter decays critically slowly in a power law ∝t(-1/2), and the other is connected to the existence of nonthermal antiferromagnetic order in systems with effective temperature above the thermal critical temperature. The frequency of the amplitude mode extrapolates to zero as one approaches the nonthermal (quasi)critical point, and thermalization is significantly delayed by the trapping in the nonthermal state. A slow relaxation of the nonthermal order is followed by a faster thermalization process.
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Affiliation(s)
- Naoto Tsuji
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
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24
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Dalla Torre EG, Demler E, Polkovnikov A. Universal rephasing dynamics after a quantum quench via sudden coupling of two initially independent condensates. PHYSICAL REVIEW LETTERS 2013; 110:090404. [PMID: 23496694 DOI: 10.1103/physrevlett.110.090404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2012] [Indexed: 06/01/2023]
Abstract
We consider a quantum quench in which two initially independent condensates are suddenly coupled and study the subsequent "rephasing" dynamics. For weak tunneling couplings, the time evolution of physical observables is predicted to follow universal scaling laws, connecting the short-time dynamics to the long-time nonperturbative regime. We first present a two-mode model valid in two and three dimensions and then move to one dimension, where the problem is described by a gapped sine-Gordon theory. Combining analytical and numerical methods, we compute universal time-dependent expectation values, allowing a quantitative comparison with future experiments.
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25
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Arrigoni E, Knap M, von der Linden W. Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach. PHYSICAL REVIEW LETTERS 2013; 110:086403. [PMID: 23473180 DOI: 10.1103/physrevlett.110.086403] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2012] [Indexed: 06/01/2023]
Abstract
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
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Affiliation(s)
- Enrico Arrigoni
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria.
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26
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Mitra A. Time evolution and dynamical phase transitions at a critical time in a system of one-dimensional bosons after a quantum quench. PHYSICAL REVIEW LETTERS 2012; 109:260601. [PMID: 23368544 DOI: 10.1103/physrevlett.109.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2012] [Revised: 09/30/2012] [Indexed: 06/01/2023]
Abstract
A renormalization group approach is used to show that a one-dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light cone increases as a nonanalytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time dependent, crucially affecting the time evolution of the system. Explicit results are presented for the time evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.
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Affiliation(s)
- Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
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27
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Sonner J, Green AG. Hawking radiation and nonequilibrium quantum critical current noise. PHYSICAL REVIEW LETTERS 2012; 109:091601. [PMID: 23002819 DOI: 10.1103/physrevlett.109.091601] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2012] [Revised: 05/24/2012] [Indexed: 06/01/2023]
Abstract
The dynamical scaling of quantum critical systems in thermal equilibrium may be inherited in the driven steady state, leading to universal out-of-equilibrium behavior. This attractive notion has been demonstrated in just a few cases. We demonstrate how holography-a mapping between the quantum critical system and a gravity dual-provides an illuminating perspective and new results. Nontrivial out-of-equilibrium universality is particularly apparent in current noise, which is dual to Hawking radiation in the gravitational system. We calculate this in a two-dimensional system driven by a strong in-plane electric field and deduce a universal scaling function interpolating between previously established equilibrium and far-from-equilibrium current noise. Since this applies at all fields, out-of-equilibrium experiments no longer require very high fields for comparison with theory.
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Affiliation(s)
- Julian Sonner
- DAMTP, University of Cambridge, United Kingdom and Imperial College London, London, United Kingdom.
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28
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Kirchner S, Si Q. Quantum criticality out of equilibrium: steady state in a magnetic single-electron transistor. PHYSICAL REVIEW LETTERS 2009; 103:206401. [PMID: 20365995 DOI: 10.1103/physrevlett.103.206401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2008] [Indexed: 05/29/2023]
Abstract
Quantum critical systems out of equilibrium are of extensive interest, but are difficult to study theoretically. We consider here the steady-state limit of a single-electron transistor with ferromagnetic leads. In equilibrium (i.e., bias voltage V = 0), this system features a continuous quantum phase transition with a critical destruction of the Kondo effect. We construct an exact quantum Boltzmann treatment in a dynamical large-N limit, and determine the universal scaling functions of both the nonlinear conductance and fluctuation-dissipation ratios. We also elucidate the decoherence properties as encoded in the local spin response.
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Affiliation(s)
- Stefan Kirchner
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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29
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Rost AW, Perry RS, Mercure JF, Mackenzie AP, Grigera SA. Entropy Landscape of Phase Formation Associated with Quantum Criticality in Sr
3
Ru
2
O
7. Science 2009; 325:1360-3. [DOI: 10.1126/science.1176627] [Citation(s) in RCA: 121] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- A. W. Rost
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
| | - R. S. Perry
- SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK
| | - J.-F. Mercure
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
| | - A. P. Mackenzie
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
| | - S. A. Grigera
- Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK
- Instituto de Física de Líquidos y Sistemas Biológicos, Universidad Nacional de La Plata–Consejo Nacional de Investigaciones Científicas y Técnicas, 1900 La Plata, Argentina
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30
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Chung CH, Le Hur K, Vojta M, Wölfle P. Nonequilibrium transport at a dissipative quantum phase transition. PHYSICAL REVIEW LETTERS 2009; 102:216803. [PMID: 19519125 DOI: 10.1103/physrevlett.102.216803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2008] [Indexed: 05/27/2023]
Abstract
We investigate the nonequilibrium transport near a quantum phase transition in a generic and relatively simple model, the dissipative resonant level model, that has many applications for nanosystems. We formulate a rigorous mapping and apply a controlled frequency-dependent renormalization group approach to compute the nonequilibrium current in the presence of a finite bias voltage V and a finite temperature T. For V-->0, we find that the conductance has its well-known equilibrium form, while it displays a distinct nonequilibrium profile at finite voltage.
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Affiliation(s)
- Chung-Hou Chung
- Electrophysics Department, National Chiao-Tung University, HsinChu, Taiwan
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31
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Aron C, Biroli G, Cugliandolo LF. Driven quantum coarsening. PHYSICAL REVIEW LETTERS 2009; 102:050404. [PMID: 19257491 DOI: 10.1103/physrevlett.102.050404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2008] [Indexed: 05/27/2023]
Abstract
We study the driven dynamics of quantum coarsening. We analyze models of M-component rotors coupled to two electronic reservoirs at different chemical potential that generate a current threading through the system. In the large M limit, we derive the dynamical phase diagram as a function of temperature, strength of quantum fluctuations, voltage, and coupling to the leads. We show that the slow relaxation in the ordering phase is universal. On large time and length scales, the dynamics are analogous to stochastic classical ones, even for the quantum system driven out of equilibrium at zero temperature. We argue that our results apply to generic driven quantum coarsening.
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Affiliation(s)
- Camille Aron
- Université Pierre et Marie Curie - Paris VI, LPTHE UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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32
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Prosen T, Pizorn I. Quantum phase transition in a far-from-equilibrium steady state of an XY spin chain. PHYSICAL REVIEW LETTERS 2008; 101:105701. [PMID: 18851227 DOI: 10.1103/physrevlett.101.105701] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2008] [Revised: 06/24/2008] [Indexed: 05/26/2023]
Abstract
Using quantization in the Fock space of operators, we compute the nonequilibrium steady state in an open Heisenberg XY spin 1/2 chain of a finite but large size coupled to Markovian baths at its ends. Numerical and theoretical evidence is given for a far-from-equilibrium quantum phase transition with the spontaneous emergence of long-range order in spin-spin correlation functions, characterized by a transition from saturation to linear growth with the size of the entanglement entropy in operator space.
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Affiliation(s)
- Tomaz Prosen
- Department of Physics, FMF, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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33
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Jakobs SG, Meden V, Schoeller H. Nonequilibrium functional renormalization group for interacting quantum systems. PHYSICAL REVIEW LETTERS 2007; 99:150603. [PMID: 17995151 DOI: 10.1103/physrevlett.99.150603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2007] [Indexed: 05/25/2023]
Abstract
We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.
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Affiliation(s)
- Severin G Jakobs
- Institut für Theoretische Physik A, RWTH Aachen, D-52056 Aachen, Germany
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