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Khastehdel Fumani F, Mahdavifar S, Afrousheh K. Entangled unique coherent line in the ground-state phase diagram of the spin-1/2 XX chain model with three-spin interaction. Phys Rev E 2024; 109:044142. [PMID: 38755842 DOI: 10.1103/physreve.109.044142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2023] [Accepted: 03/19/2024] [Indexed: 05/18/2024]
Abstract
Entangled spin coherent states are a type of quantum states that involve two or more spin systems that are correlated in a nonclassical way. These states can improve metrology and information processing, as they can surpass the standard quantum limit, which is the ultimate bound for precision measurements using coherent states. However, finding entangled coherent states in physical systems is challenging because they require precise control and manipulation of the interactions between the modes. In this work we show that entangled unique coherent states can be found in the ground state of the spin-1/2 XX chain model with three-spin interaction, which is an exactly solvable model in quantum magnetism. We use the spin squeezing parameter, the l_{1}-norm of coherence, and the entanglement entropy as tools to detect and characterize these unique coherent states. We find that these unique coherent states exist in a gapless spin liquid phase, where they form a line that separates two regions with different degrees of squeezing. We call this line the entangled unique coherent line, as it corresponds to the almost maximum entanglement between two halves of the system. We also study the critical scaling of the spin squeezing parameter and the entanglement entropy versus the system size.
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Affiliation(s)
- F Khastehdel Fumani
- Department of Basic Sciences, Langarud Branch, Islamic Azad University, 4471311127 Langarud, Iran
| | - S Mahdavifar
- Department of Physics, University of Guilan, 41335-1914 Rasht, Iran
| | - K Afrousheh
- Department of Physics, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait
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2
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Khalouf-Rivera J, Gamito J, Pérez-Bernal F, Arias JM, Pérez-Fernández P. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Dynamical aspects. Phys Rev E 2023; 107:064134. [PMID: 37464676 DOI: 10.1103/physreve.107.064134] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 06/07/2023] [Indexed: 07/20/2023]
Abstract
The standard Lipkin-Meshkov-Glick (LMG) model undergoes a second-order ground-state quantum phase transition (QPT) and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the LMG Hamiltonian gives rise to a second ESQPT that alters the static properties of the model [Gamito et al., Phys. Rev. E 106, 044125 (2022)2470-004510.1103/PhysRevE.106.044125]. In the present work, the dynamical implications associated to this new ESQPT are analyzed. For that purpose, a quantum quench protocol is defined on the system Hamiltonian that takes an initial state, usually the ground state, into a complex excited state that evolves on time. The impact of the new ESQPT on the time evolution of the survival probability and the local density of states after the quantum quench, as well as on the Loschmidt echoes and the microcanonical out-of-time-order correlator (OTOC) are discussed. The anharmonity-induced ESQPT, despite having a different physical origin, has dynamical consequences similar to those observed in the ESQPT already present in the standard LMG model.
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Affiliation(s)
- J Khalouf-Rivera
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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3
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Sauerwein N, Orsi F, Uhrich P, Bandyopadhyay S, Mattiotti F, Cantat-Moltrecht T, Pupillo G, Hauke P, Brantut JP. Engineering random spin models with atoms in a high-finesse cavity. NATURE PHYSICS 2023; 19:1128-1134. [PMID: 37575364 PMCID: PMC10415180 DOI: 10.1038/s41567-023-02033-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 03/23/2023] [Indexed: 08/15/2023]
Abstract
All-to-all interacting, disordered quantum many-body models have a wide range of applications across disciplines, from spin glasses in condensed-matter physics over holographic duality in high-energy physics to annealing algorithms in quantum computing. Typically, these models are abstractions that do not find unambiguous physical realizations in nature. Here we realize an all-to-all interacting, disordered spin system by subjecting an atomic cloud in a cavity to a controllable light shift. Adjusting the detuning between atom resonance and cavity mode, we can tune between disordered versions of a central-mode model and a Lipkin-Meshkov-Glick model. By spectroscopically probing the low-energy excitations of the system, we explore the competition of interactions with disorder across a broad parameter range. We show how disorder in the central-mode model breaks the strong collective coupling, making the dark-state manifold cross over to a random distribution of weakly mixed light-matter, 'grey', states. In the Lipkin-Meshkov-Glick model, the ferromagnetic finite-sized ground state evolves towards a paramagnet as disorder is increased. In that regime, semi-localized eigenstates emerge, as we observe by extracting bounds on the participation ratio. These results present substantial steps towards freely programmable cavity-mediated interactions for the design of arbitrary spin Hamiltonians.
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Affiliation(s)
- Nick Sauerwein
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Francesca Orsi
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Philipp Uhrich
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Soumik Bandyopadhyay
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Francesco Mattiotti
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Tigrane Cantat-Moltrecht
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Guido Pupillo
- University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006), aQCess, Strasbourg, France
| | - Philipp Hauke
- Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Jean-Philippe Brantut
- Institute of Physics and Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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Gamito J, Khalouf-Rivera J, Arias JM, Pérez-Fernández P, Pérez-Bernal F. Excited-state quantum phase transitions in the anharmonic Lipkin-Meshkov-Glick model: Static aspects. Phys Rev E 2022; 106:044125. [PMID: 36397542 DOI: 10.1103/physreve.106.044125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 08/15/2022] [Indexed: 06/16/2023]
Abstract
The basic Lipkin-Meshkov-Glick model displays a second-order ground-state quantum phase transition and an excited-state quantum phase transition (ESQPT). The inclusion of an anharmonic term in the Hamiltonian implies a second ESQPT of a different nature. We characterize this ESQPT using the mean field limit of the model. The alternative ESQPT, associated with the changes in the boundary of the finite Hilbert space of the system, can be properly described using the order parameter of the ground-state quantum phase transition, the energy gap between adjacent states, the participation ratio, and the quantum fidelity susceptibility.
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Affiliation(s)
- J Gamito
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
| | - J Khalouf-Rivera
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
| | - J M Arias
- Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
| | - P Pérez-Fernández
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
- Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain
| | - F Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain
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Wang Q, Pérez-Bernal F. Signatures of excited-state quantum phase transitions in quantum many-body systems: Phase space analysis. Phys Rev E 2021; 104:034119. [PMID: 34654165 DOI: 10.1103/physreve.104.034119] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2021] [Accepted: 08/31/2021] [Indexed: 11/07/2022]
Abstract
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China and CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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6
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Bao J, Liu YH, Guo B. Global quantum discord in the Lipkin-Meshkov-Glick model at zero and finite temperatures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:495401. [PMID: 34517354 DOI: 10.1088/1361-648x/ac2647] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
We study the global quantum discord (GQD) in the Lipkin-Meshkov-Glick (LMG) model at zero and finite temperatures, in which all spins are mutually interacted and introduced in an external magnetic field (denoted byh). We confirm that the high coordinate number is one of the most distinguishing features of the LMG model, which directly results in the nontrivial behaviors of quantum correlations. We compare the GQD with other quantum correlations measures (such as concurrence, quantum discord, and global entanglement) and find the remarkable difference between them. For instance, we find that GQD spreads in the entire system and captures more information on quantum correlations when comparing with concurrence and quantum (pairwise) discord. We discover that GQD can characterize multipartite correlations in the both broken phase (h< 1) and the symmetric phase (h⩾ 1), while global entanglement and its generalized fail. Moreover, we show that the ground-state GQD can identify second-order quantum phase transitions of the LMG model in the thermodynamic limit. By making the scaling behavior of the GQD in the LMG model analysis, we show that GQD (denoted byG) scales asG∼k⋅N+cwithk> 0 in the anisotropic cases for any fixed magnetic field. We further show that GQD behaves asG|sn∼k⋅1N+cwithk< 0 in the isotropic cases for any Dicke state |sn⟩. Hereinkandcare the fitting parameters. We also find that the thermal stability of the GQD at low temperatures depends on the energy gap. We further reveal that the extraordinary behaviors of the thermal-state GQD in the isotropic LMG model are explained by the contribution theory of the energy levels.
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Affiliation(s)
- Jia Bao
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Yan-Hong Liu
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
| | - Bin Guo
- Department of Physics, Wuhan University of Technology, Wuhan 430070, People's Republic of China
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7
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Wang Q, Pérez-Bernal F. Characterizing the Lipkin-Meshkov-Glick model excited-state quantum phase transition using dynamical and statistical properties of the diagonal entropy. Phys Rev E 2021; 103:032109. [PMID: 33862777 DOI: 10.1103/physreve.103.032109] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 02/17/2021] [Indexed: 06/12/2023]
Abstract
Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.
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Affiliation(s)
- Qian Wang
- Department of Physics, Zhejiang Normal University, Jinhua 321004, China and CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, SI-2000 Maribor, Slovenia
| | - Francisco Pérez-Bernal
- Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física, Matemáticas y Computación, Universidad de Huelva, Huelva 21071, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Granada 18071, Spain
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8
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Mao BB, Li L, You WL, Liu M. Superradiant phase transition in quantum Rabi dimer with staggered couplings. PHYSICA A: STATISTICAL MECHANICS AND ITS APPLICATIONS 2021; 564:125534. [DOI: 10.1016/j.physa.2020.125534] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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Titum P, Maghrebi MF. Nonequilibrium Criticality in Quench Dynamics of Long-Range Spin Models. PHYSICAL REVIEW LETTERS 2020; 125:040602. [PMID: 32794797 DOI: 10.1103/physrevlett.125.040602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2019] [Revised: 06/07/2020] [Accepted: 06/19/2020] [Indexed: 06/11/2023]
Abstract
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.
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Affiliation(s)
- Paraj Titum
- Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland 20723, USA
- 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
| | - Mohammad F Maghrebi
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Muñoz-Arias MH, Poggi PM, Jessen PS, Deutsch IH. Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback. PHYSICAL REVIEW LETTERS 2020; 124:110503. [PMID: 32242733 DOI: 10.1103/physrevlett.124.110503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
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Affiliation(s)
- Manuel H Muñoz-Arias
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Pablo M Poggi
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Poul S Jessen
- Center for Quantum Information and Control, CQuIC, College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Ivan H Deutsch
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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