1
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Das AK, Ghosh A, Khaymovich IM. Absence of Mobility Edge in Short-Range Uncorrelated Disordered Model: Coexistence of Localized and Extended States. PHYSICAL REVIEW LETTERS 2023; 131:166401. [PMID: 37925734 DOI: 10.1103/physrevlett.131.166401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 08/26/2023] [Indexed: 11/07/2023]
Abstract
Unlike the well-known Mott's argument that extended and localized states should not coexist at the same energy in a generic random potential, we formulate the main principles and provide an example of a nearest-neighbor tight-binding disordered model which carries both localized and extended states without forming the mobility edge. Unexpectedly, this example appears to be given by a well-studied β ensemble with independently distributed random diagonal potential and inhomogeneous kinetic hopping terms. In order to analytically tackle the problem, we locally map the above model to the 1D Anderson model with matrix-size- and position-dependent hopping and confirm the coexistence of localized and extended states, which is shown to be robust to the perturbations of both potential and kinetic terms due to the separation of the above states in space. In addition, the mapping shows that the extended states are nonergodic and allows one to analytically estimate their fractal dimensions.
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Affiliation(s)
- Adway Kumar Das
- Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246 India
| | - Anandamohan Ghosh
- Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246 India
| | - Ivan M Khaymovich
- Nordita, Stockholm University and KTH Royal Institute of Technology Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden and Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
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2
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Sinha A. Development of research network on Quantum Annealing Computation and Information using Google Scholar data. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210413. [PMID: 36463919 DOI: 10.1098/rsta.2021.0413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 09/08/2022] [Indexed: 06/17/2023]
Abstract
We build and analyse the network of 100 top-cited nodes (research papers and books from Google Scholar; the strength or citation of the nodes range from about 44 000 up to 100) starting in early 1980 until last year. These searched publications (papers and books) are based on Quantum Annealing Computation and Information categorized into four different sets: (A) Quantum/Transverse Field Spin Glass Model, (B) Quantum Annealing, (C) Quantum Adiabatic Computation and (D) Quantum Computation Information in the title or abstract of the searched publications. We fitted the growth in the annual number of publication ([Formula: see text]) in each of these four categories, A-D, to the form [Formula: see text] where [Formula: see text] denotes the time in years. We found the scaling time [Formula: see text] to be of the order of about 10 years for categories A and C, whereas [Formula: see text] is of the order of about 5 years for categories B and D. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Antika Sinha
- Department of Computer Science, Asutosh College, Kolkata, West Bengal 700026, India
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3
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Many-body localization enables iterative quantum optimization. Nat Commun 2022; 13:5503. [PMID: 36127344 PMCID: PMC9489738 DOI: 10.1038/s41467-022-33179-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 09/07/2022] [Indexed: 11/08/2022] Open
Abstract
Many discrete optimization problems are exponentially hard due to the underlying glassy landscape. This means that the optimization cost exhibits multiple local minima separated by an extensive number of switched discrete variables. Quantum computation was coined to overcome this predicament, but so far had only a limited progress. Here we suggest a quantum approximate optimization algorithm which is based on a repetitive cycling around the tricritical point of the many-body localization (MBL) transition. Each cycle includes quantum melting of the glassy state through a first order transition with a subsequent reentrance through the second order MBL transition. Keeping the reentrance path sufficiently close to the tricritical point separating the first and second order transitions, allows one to systematically improve optimization outcomes. The running time of this algorithm scales algebraically with the system size and the required precision. The corresponding exponents are related to critical indexes of the continuous MBL transition. There are several proposals for quantum algorithms solving optimisation problems, but so far none of them has provided a clear speedup. Here, the authors propose an iterative protocol featuring periodic cycling around the tricritical point of a many-body localization transition.
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4
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Leschke H, Manai C, Ruder R, Warzel S. Existence of Replica-Symmetry Breaking in Quantum Glasses. PHYSICAL REVIEW LETTERS 2021; 127:207204. [PMID: 34860058 DOI: 10.1103/physrevlett.127.207204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Revised: 08/29/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a "transverse" magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multispin interactions, sometimes dubbed as the transverse p-spin model.
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Affiliation(s)
- Hajo Leschke
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Chokri Manai
- Department of Mathematics and Munich Center for Quantum Science and Technology, TU München, 85747 Garching, Germany
| | - Rainer Ruder
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Simone Warzel
- Departments of Mathematics and Physics, Munich Center for Quantum Science and Technology, TU München, 85747 Garching, Germany
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5
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Thomson SJ, Urbani P, Schiró M. Quantum Quenches in Isolated Quantum Glasses out of Equilibrium. PHYSICAL REVIEW LETTERS 2020; 125:120602. [PMID: 33016769 DOI: 10.1103/physrevlett.125.120602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2019] [Revised: 07/23/2020] [Accepted: 08/19/2020] [Indexed: 06/11/2023]
Abstract
In this work, we address the question of how a closed quantum system thermalizes in the presence of a random external potential. By investigating the quench dynamics of the isolated quantum spherical p-spin model, a paradigmatic model of a mean-field glass, we aim to shed new light on this complex problem. Employing a closed-time Schwinger-Keldysh path integral formalism, we first initialize the system in a random, infinite-temperature configuration and allow it to equilibrate in contact with a thermal bath before switching off the bath and performing a quench. We find evidence that increasing the strength of either the interactions or the quantum fluctuations can act to lower the effective temperature of the isolated system and stabilize glassy behavior.
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Affiliation(s)
- S J Thomson
- Centre de Physique Théorique, CNRS, Institut Polytechnique de Paris, Route de Saclay, F-91128 Palaiseau, France
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France
| | - P Urbani
- Université Paris-Saclay, CNRS, CEA, Institut de physique théorique, 91191, Gif-sur-Yvette, France
| | - M Schiró
- JEIP, USR 3573 CNRS, Collège de France, PSL University, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
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6
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Mierzejewski M, Prelovšek P, Bonča J. Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime. PHYSICAL REVIEW LETTERS 2019; 122:206601. [PMID: 31172751 DOI: 10.1103/physrevlett.122.206601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2018] [Indexed: 06/09/2023]
Abstract
A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.
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Affiliation(s)
- M Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - P Prelovšek
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - J Bonča
- J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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7
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Chen C, Burnell F, Chandran A. How Does a Locally Constrained Quantum System Localize? PHYSICAL REVIEW LETTERS 2018; 121:085701. [PMID: 30192622 DOI: 10.1103/physrevlett.121.085701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2017] [Indexed: 06/08/2023]
Abstract
At low energy, the dynamics of excitations of many physical systems are locally constrained. Examples include frustrated antiferromagnets, fractional quantum Hall fluids, and Rydberg atoms in the blockaded regime. Can such locally constrained systems be fully many-body localized? In this Letter, we answer this question affirmatively and elucidate the structure of the accompanying quasilocal integrals of motion. By studying disordered spin chains subject to a projection constraint in the z direction, we show that full many-body localization (MBL) is stable at strong z-field disorder and identify a new mechanism of localization through resonance at strong transverse disorder. However, MBL is not guaranteed; the constraints can "frustrate" the tendency of the spins to align with the transverse fields and lead to full thermalization or criticality. We further provide evidence that the transition is discontinuous in local observables with large sample-to-sample variations. Our dynamical phase diagram is accessible in current Rydberg atomic experiments which realize programmable constrained Ising Hamiltonians.
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Affiliation(s)
- Chun Chen
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Fiona Burnell
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Anushya Chandran
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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8
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Lan Z, van Horssen M, Powell S, Garrahan JP. Quantum Slow Relaxation and Metastability due to Dynamical Constraints. PHYSICAL REVIEW LETTERS 2018; 121:040603. [PMID: 30095948 DOI: 10.1103/physrevlett.121.040603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 05/24/2018] [Indexed: 06/08/2023]
Abstract
One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow thermalization and metastability in translationally invariant quantum many-body systems. We illustrate this general idea by considering two simple models: (i) a one-dimensional quantum analogue to classical constrained lattice gases where excitation hopping is constrained by the state of neighboring sites, mimicking excluded-volume interactions of dense fluids; and (ii) fully packed quantum dimers on the square lattice. Both models have a Rokhsar-Kivelson (RK) point at which kinetic and potential energy constants are equal. To one side of the RK point, where kinetic energy dominates, thermalization is fast. To the other, where potential energy dominates, thermalization is slow, memory of initial conditions persists for long times, and separation of timescales leads to pronounced metastability before eventual thermalization. Furthermore, in analogy with what occurs in the relaxation of classical glasses, the slow-thermalization regime displays dynamical heterogeneity as manifested by spatially segregated growth of entanglement.
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Affiliation(s)
- Zhihao Lan
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Merlijn van Horssen
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Stephen Powell
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Juan P Garrahan
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems and School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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9
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Lemut G, Mierzejewski M, Bonča J. Complete Many-Body Localization in the t-J Model Caused by a Random Magnetic Field. PHYSICAL REVIEW LETTERS 2017; 119:246601. [PMID: 29286750 DOI: 10.1103/physrevlett.119.246601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2017] [Indexed: 06/07/2023]
Abstract
The many body localization (MBL) of spin-1/2 fermions poses a challenging problem. It is known that the disorder in the charge sector may be insufficient to cause full MBL. Here, we study dynamics of a single hole in one dimensional t-J model subject to a random magnetic field. We show that strong disorder that couples only to the spin sector localizes both spin and charge degrees of freedom. Charge localization is confirmed also for a finite concentration of holes. While we cannot precisely pinpoint the threshold disorder, we conjecture that there are two distinct transitions. Weaker disorder first causes localization in the spin sector. Carriers become localized for somewhat stronger disorder, when the spin localization length is of the order of a single lattice spacing.
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Affiliation(s)
- Gal Lemut
- J. Stefan Institute, 1000 Ljubljana, Slovenia
| | - Marcin Mierzejewski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Janez Bonča
- J. Stefan Institute, 1000 Ljubljana, Slovenia
- Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia
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10
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Mossi G, Scardicchio A. Ergodic and localized regions in quantum spin glasses on the Bethe lattice. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160424. [PMID: 29084889 PMCID: PMC5665780 DOI: 10.1098/rsta.2016.0424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 06/19/2017] [Indexed: 06/07/2023]
Abstract
By considering the quantum dynamics of a transverse-field Ising spin glass on the Bethe lattice, we find the existence of a many-body localized (MBL) region at small transverse field and low temperature. The region is located within the thermodynamic spin glass phase. Accordingly, we conjecture that quantum dynamics inside the glassy region is split into a small MBL region and a large delocalized (but not necessarily ergodic) region. This has implications for the analysis of the performance of quantum adiabatic algorithms.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- G Mossi
- SISSA, Via Bonomea 265, 34136 Trieste, Italy
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
| | - A Scardicchio
- INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
- Abdus Salam ICTP Trieste, Strada Costiera 11, 34151 Trieste, Italy
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11
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Ponte P, Laumann CR, Huse DA, Chandran A. Thermal inclusions: how one spin can destroy a many-body localized phase. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:20160428. [PMID: 29084891 PMCID: PMC5665782 DOI: 10.1098/rsta.2016.0428] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/11/2017] [Indexed: 06/07/2023]
Abstract
Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N≫1 localized bits subject to random fields. On increasing J, the system transitions from an MBL to a delocalized phase on the vanishing scale Jc(N)∼1/N, up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either 'on' (strongly entangled) or 'off' (weakly entangled) in eigenstates. The clusters of 'on' bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
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Affiliation(s)
- Pedro Ponte
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
- Department of Physics and Astronomy, University of Waterloo, Ontario, Canada N2L 3G1
| | - C R Laumann
- Department of Physics, Boston University, Boston, MA 02215, USA
| | - David A Huse
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - A Chandran
- Department of Physics, Boston University, Boston, MA 02215, USA
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12
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Altland A, Micklitz T. Field Theory Approach to Many-Body Localization. PHYSICAL REVIEW LETTERS 2017; 118:127202. [PMID: 28388186 DOI: 10.1103/physrevlett.118.127202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/07/2023]
Abstract
We introduce an analytic approach to many-body localization (MBL) in random spin chains. We consider MBL within a first quantized framework where it becomes a localization phenomenon in the high-dimensional lattice defined by the Hilbert space of the clean system. Designed in analogy with the field-theory description of single particle localization, our approach describes wave package propagation on that lattice after a disorder average has been performed and the system is controlled by only a few universal parameters. We discuss the stability of an ergodic weak disorder and a localized strong disorder phase, respectively, and demonstrate that the latter is protected by mechanisms which put MBL outside the universality class of Anderson localization.
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Affiliation(s)
- Alexander Altland
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany
| | - Tobias Micklitz
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
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13
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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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14
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Smelyanskiy VN, Venturelli D, Perdomo-Ortiz A, Knysh S, Dykman MI. Quantum Annealing via Environment-Mediated Quantum Diffusion. PHYSICAL REVIEW LETTERS 2017; 118:066802. [PMID: 28234537 DOI: 10.1103/physrevlett.118.066802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2016] [Indexed: 06/06/2023]
Abstract
We show that quantum diffusion near a quantum critical point can provide an efficient mechanism of quantum annealing. It is based on the diffusion-mediated recombination of excitations in open systems far from thermal equilibrium. We find that, for an Ising spin chain coupled to a bosonic bath and driven by a monotonically decreasing transverse field, excitation diffusion sharply slows down below the quantum critical region. This leads to spatial correlations and effective freezing of the excitation density. Still, obtaining an approximate solution of an optimization problem via the diffusion-mediated quantum annealing can be faster than via closed-system quantum annealing or Glauber dynamics.
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Affiliation(s)
| | - Davide Venturelli
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
| | - Alejandro Perdomo-Ortiz
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
| | - Sergey Knysh
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
- Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA
| | - Mark I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-2320, USA
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15
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Isakov SV, Mazzola G, Smelyanskiy VN, Jiang Z, Boixo S, Neven H, Troyer M. Understanding Quantum Tunneling through Quantum Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2016; 117:180402. [PMID: 27835027 DOI: 10.1103/physrevlett.117.180402] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Indexed: 05/02/2023]
Abstract
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is O(Δ^{2}), where Δ is the tunneling splitting (or equivalently the minimum spectral gap). An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC simulations, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture.
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Affiliation(s)
| | | | | | - Zhang Jiang
- QuAIL, NASA Ames Research Center, Moffett Field, California 94035, USA
- Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, Maryland 20770, USA
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16
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Levi E, Heyl M, Lesanovsky I, Garrahan JP. Robustness of Many-Body Localization in the Presence of Dissipation. PHYSICAL REVIEW LETTERS 2016; 116:237203. [PMID: 27341255 DOI: 10.1103/physrevlett.116.237203] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2015] [Indexed: 06/06/2023]
Abstract
Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.
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Affiliation(s)
- Emanuele Levi
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - Markus Heyl
- Physik Department, Technische Universität München, 85747 Garching, Germany
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
| | - Juan P Garrahan
- School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom
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17
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Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances. ENTROPY 2016. [DOI: 10.3390/e18040122] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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18
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Yang ZC, Chamon C, Hamma A, Mucciolo ER. Two-Component Structure in the Entanglement Spectrum of Highly Excited States. PHYSICAL REVIEW LETTERS 2015; 115:267206. [PMID: 26765022 DOI: 10.1103/physrevlett.115.267206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Indexed: 06/05/2023]
Abstract
We study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a "two-component" structure: a universal part that is associated with random matrix theory, and a nonuniversal part that is model dependent. The nonuniversal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the eigenstate thermalization hypothesis holds. The fraction of the spectrum containing the universal part decreases as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct an order parameter for measuring the degree of randomness of a generic highly excited state, which is also a promising candidate for studying the many-body localization transition. Two toy models based on Rokhsar-Kivelson type wave functions are constructed and their entanglement spectra are shown to exhibit the same structure.
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Affiliation(s)
- Zhi-Cheng Yang
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
| | - Claudio Chamon
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
| | - Alioscia Hamma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Eduardo R Mucciolo
- Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
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19
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Devakul T, Singh RRP. Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition. PHYSICAL REVIEW LETTERS 2015; 115:187201. [PMID: 26565492 DOI: 10.1103/physrevlett.115.187201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2015] [Indexed: 06/05/2023]
Abstract
We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.
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Affiliation(s)
- Trithep Devakul
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Rajiv R P Singh
- Department of Physics, University of California Davis, Davis, California 95616, USA
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20
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De Luca A, Rosso A. Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization. PHYSICAL REVIEW LETTERS 2015; 115:080401. [PMID: 26340169 DOI: 10.1103/physrevlett.115.080401] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Indexed: 06/05/2023]
Abstract
Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.
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Affiliation(s)
- Andrea De Luca
- Laboratoire de Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université Paris-Sud, Bât. 100, 15 rue Georges Clémenceau, 91405 Orsay Cedex, France
| | - Alberto Rosso
- Laboratoire de Physique Théorique et Modèles Statistiques (UMR CNRS 8626), Université Paris-Sud, Bât. 100, 15 rue Georges Clémenceau, 91405 Orsay Cedex, France
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21
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Bera S, Schomerus H, Heidrich-Meisner F, Bardarson JH. Many-Body Localization Characterized from a One-Particle Perspective. PHYSICAL REVIEW LETTERS 2015; 115:046603. [PMID: 26252702 DOI: 10.1103/physrevlett.115.046603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2015] [Indexed: 05/16/2023]
Abstract
We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.
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Affiliation(s)
- Soumya Bera
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Henning Schomerus
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
- Department of Physics, Lancaster University, LA1 4YB Lancaster, United Kingdom
| | - Fabian Heidrich-Meisner
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany
| | - Jens H Bardarson
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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22
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Lazarides A, Das A, Moessner R. Fate of Many-Body Localization Under Periodic Driving. PHYSICAL REVIEW LETTERS 2015; 115:030402. [PMID: 26230771 DOI: 10.1103/physrevlett.115.030402] [Citation(s) in RCA: 62] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2014] [Indexed: 06/04/2023]
Abstract
We study many-body localized quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalization for any driving strength and frequency. By contrast, for a fully localized many-body system, a delocalization transition occurs at a finite driving frequency. We present numerical studies on a system of interacting one-dimensional bosons and the quantum random energy model, as well as simple physical pictures accounting for those results.
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Affiliation(s)
| | - Arnab Das
- Theoretical Physics Department, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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23
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Agarwal K, Gopalakrishnan S, Knap M, Müller M, Demler E. Anomalous diffusion and griffiths effects near the many-body localization transition. PHYSICAL REVIEW LETTERS 2015; 114:160401. [PMID: 25955037 DOI: 10.1103/physrevlett.114.160401] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2014] [Indexed: 06/04/2023]
Abstract
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.
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Affiliation(s)
- Kartiek Agarwal
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | | | - Michael Knap
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - Markus Müller
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Eugene Demler
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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