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Mu S, Gong J, Lemarié G. Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets. PHYSICAL REVIEW LETTERS 2024; 132:046301. [PMID: 38335351 DOI: 10.1103/physrevlett.132.046301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 09/08/2023] [Accepted: 12/14/2023] [Indexed: 02/12/2024]
Abstract
We identify the key features of Kardar-Parisi-Zhang (KPZ) universality class in the fluctuations of the wave density logarithm in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of 1/3, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent 2/3. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched exponential correction to its well-known exponential localization.
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Affiliation(s)
- Sen Mu
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
| | - Jiangbin Gong
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China
| | - Gabriel Lemarié
- Department of Physics, National University of Singapore, Singapore 117542, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, France
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Baldwin CL, Laumann CR, Pal A, Scardicchio A. Clustering of Nonergodic Eigenstates in Quantum Spin Glasses. PHYSICAL REVIEW LETTERS 2017; 118:127201. [PMID: 28388188 DOI: 10.1103/physrevlett.118.127201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Indexed: 06/07/2023]
Abstract
The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p-spin models of the spin-glass theory, eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.
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Affiliation(s)
- C L Baldwin
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - C R Laumann
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
| | - A Pal
- Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford OX1 3NP, United Kingdom
| | - A Scardicchio
- Abdus Salam ICTP Trieste, Strada Costiera 11, 34151 Trieste, Italy
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
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Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions. Sci Rep 2017; 7:44044. [PMID: 28300065 PMCID: PMC5353753 DOI: 10.1038/srep44044] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Accepted: 01/31/2017] [Indexed: 11/08/2022] Open
Abstract
We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.
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Doron A, Tamir I, Mitra S, Zeltzer G, Ovadia M, Shahar D. Nonequilibrium Second-Order Phase Transition in a Cooper-Pair Insulator. PHYSICAL REVIEW LETTERS 2016; 116:057001. [PMID: 26894728 DOI: 10.1103/physrevlett.116.057001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2015] [Indexed: 06/05/2023]
Abstract
In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.
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Affiliation(s)
- A Doron
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - I Tamir
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - S Mitra
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - G Zeltzer
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - M Ovadia
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - D Shahar
- Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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Abstract
In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the “superinsulating” phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T < 0.04 K. We discuss our results in the light of theories that lead to a finite-T insulator.
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Chudnovsky EM. Instanton glass generated by noise in a Josephson-junction array. PHYSICAL REVIEW LETTERS 2009; 103:137001. [PMID: 19905536 DOI: 10.1103/physrevlett.103.137001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2009] [Indexed: 05/28/2023]
Abstract
We compute the correlation function of a superconducting order parameter in a continuous model of a two-dimensional Josephson-junction array in the presence of a weak Gaussian noise. When the Josephson coupling is large compared to the charging energy, the correlations in the Euclidian space decay exponentially at low temperatures regardless of the strength of the noise. We interpret such a state as a collective Cooper-pair insulator and argue that it resembles properties of disordered superconducting films.
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Affiliation(s)
- E M Chudnovsky
- Physics Department, Lehman College, The City University of New York, Bronx, New York 10468-1589, USA
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Ovadia M, Sacépé B, Shahar D. Electron-phonon decoupling in disordered insulators. PHYSICAL REVIEW LETTERS 2009; 102:176802. [PMID: 19518807 DOI: 10.1103/physrevlett.102.176802] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2009] [Indexed: 05/27/2023]
Abstract
The current-voltage characteristics measured in the insulating state terminating the superconducting phase in disordered superconductors exhibit sharp threshold voltages, where the current abruptly changes by as much as 5 orders of magnitude. We analyze the current-voltage characteristics of an amorphous indium oxide film in the field-tuned insulating state, and show that they are consistent with a bistability of the electron temperature, and with a significant overheating of the electron system above the lattice temperature. An analysis of these current jumps indicates that, in the insulating state, the electrons are thermally decoupled from the phonon bath.
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Affiliation(s)
- M Ovadia
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Altshuler BL, Kravtsov VE, Lerner IV, Aleiner IL. Jumps in current-voltage characteristics in disordered films. PHYSICAL REVIEW LETTERS 2009; 102:176803. [PMID: 19518808 DOI: 10.1103/physrevlett.102.176803] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2009] [Indexed: 05/27/2023]
Abstract
We argue that giant jumps of current at finite voltages observed in disordered films of InO, TiN, and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low resistive, while the other, high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance R(T) is steep enough. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of the details of the I-V characteristics does not involve adjustable parameters and turns out to be in quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture.
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Affiliation(s)
- Boris L Altshuler
- Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA
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Pergament AL, Malinenko VP, Tulubaeva OI, Aleshina LA. Electroforming and switching effects in yttrium oxide. ACTA ACUST UNITED AC 2004. [DOI: 10.1002/pssa.200306804] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Roters L, Hucht A, Lübeck S, Nowak U, Usadel KD. Depinning transition and thermal fluctuations in the random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5202-7. [PMID: 11970390 DOI: 10.1103/physreve.60.5202] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/1999] [Indexed: 04/18/2023]
Abstract
We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.
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Affiliation(s)
- L Roters
- Theoretische Tieftemperaturphysik, Gerhard-Mercator-Universität Duisburg, 47048 Duisburg, Germany.
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