1
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Xu W, Lv C, Zhou Q. Multipolar condensates and multipolar Josephson effects. Nat Commun 2024; 15:4786. [PMID: 38839836 PMCID: PMC11153559 DOI: 10.1038/s41467-024-48907-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 05/16/2024] [Indexed: 06/07/2024] Open
Abstract
When single-particle dynamics are suppressed in certain strongly correlated systems, dipoles arise as elementary carriers of quantum kinetics. These dipoles can further condense, providing physicists with a rich realm to study fracton phases of matter. Whereas recent theoretical discoveries have shown that an unconventional lattice model may host a dipole condensate as the ground state, we show that dipole condensates prevail in bosonic systems due to a self-proximity effect. Our findings allow experimentalists to manipulate the phase of a dipole condensate and deliver dipolar Josephson effects, where supercurrents of dipoles arise in the absence of particle flows. The self-proximity effects can also be utilized to produce a generic multipolar condensate. The kinetics of the n-th order multipoles unavoidably creates a condensate of the (n + 1)-th order multipoles, forming a hierarchy of multipolar condensates that will offer physicists a whole new class of macroscopic quantum phenomena.
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Affiliation(s)
- Wenhui Xu
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Chenwei Lv
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA
| | - Qi Zhou
- Department of Physics and Astronomy, Purdue University, West Lafayette, IN, 47907, USA.
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN, 47907, USA.
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2
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Atanasova H, Erpenbeck A, Gull E, Lev YB, Cohen G. Stark Many-Body Localization in Interacting Infinite Dimensional Systems. PHYSICAL REVIEW LETTERS 2024; 132:166301. [PMID: 38701447 DOI: 10.1103/physrevlett.132.166301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Revised: 03/22/2024] [Accepted: 03/29/2024] [Indexed: 05/05/2024]
Abstract
We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization at least up to time that scales exponentially with the system size. Here, we consider systems initially in a spin density wave state using a combination of numerically exact and approximate techniques. We show that for sufficiently weak electric fields, the wave's momentum component decays exponentially with time in a way consistent with normal diffusion. By studying different wavelengths, we extract the dynamical exponent and the generalized diffusion coefficient at each field strength. Interestingly, we find a nonmonotonic dependence of the dynamical exponent on the electric field. As the field increases toward a critical value proportional to the Hubbard interaction strength, transport slows down, becoming subdiffusive. At large interaction strengths, however, transport speeds up again with increasing field, exhibiting superdiffusive characteristics when the electric field is comparable to the interaction strength. Eventually, at the large field limit, localization occurs and the current through the system is suppressed.
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Affiliation(s)
| | - André Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yevgeny Bar Lev
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Guy Cohen
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
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3
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Boesl J, Zechmann P, Feldmeier J, Knap M. Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains. PHYSICAL REVIEW LETTERS 2024; 132:143401. [PMID: 38640374 DOI: 10.1103/physrevlett.132.143401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 03/15/2024] [Indexed: 04/21/2024]
Abstract
Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimensional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground-state phases. We find that, in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution and find clear signatures of the low-energy fracton dynamics.
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Affiliation(s)
- Julian Boesl
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Philip Zechmann
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Johannes Feldmeier
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Michael Knap
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
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4
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Cecile G, De Nardis J, Ilievski E. Squeezed Ensembles and Anomalous Dynamic Roughening in Interacting Integrable Chains. PHYSICAL REVIEW LETTERS 2024; 132:130401. [PMID: 38613285 DOI: 10.1103/physrevlett.132.130401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 02/28/2024] [Indexed: 04/14/2024]
Abstract
It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack magnetic fluctuations instead locally relax to squeezed generalized Gibbs ensembles governed by nonlocal equilibrium Hamiltonians, representing exotic equilibrium states with subextensive charge fluctuations that violate the self-affine scaling. At the isotropic point, we find exceptional behavior and explicit dependence on the initial state. Particularly, we find that relaxation from the Néel state is governed by extensive fluctuations and a superdiffusive dynamical exponent compatible with the Kardar-Parisi-Zhang universality. On the other hand, there are other nonfluctuating initial states that display diffusive scaling, e.g., a product state of spin singlets. Our predictions provide examples of anomalous quantum transport and fluctuations in strictly quantum states which can be directly tested in state-of-the-art cold atomic experimental settings.
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Affiliation(s)
- Guillaume Cecile
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France
| | - Jacopo De Nardis
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France
| | - Enej Ilievski
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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5
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Royen K, Mondal S, Pollmann F, Heidrich-Meisner F. Enhanced many-body localization in a kinetically constrained model. Phys Rev E 2024; 109:024136. [PMID: 38491625 DOI: 10.1103/physreve.109.024136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
In the study of the thermalization of closed quantum systems, the role of kinetic constraints on the temporal dynamics and the eventual thermalization is attracting significant interest. Kinetic constraints typically lead to long-lived metastable states depending on initial conditions. We consider a model of interacting hardcore bosons with an additional kinetic constraint that was originally devised to capture glassy dynamics at high densities. As a main result, we demonstrate that the system is highly prone to localization in the presence of uncorrelated disorder. Adding disorder quickly triggers long-lived dynamics as evidenced in the time evolution of density autocorrelations. Moreover, the kinetic constraint favors localization also in the eigenstates, where a finite-size transition to a many-body localized phase occurs for much lower disorder strengths than for the same model without a kinetic constraint. Our work sheds light on the intricate interplay of kinetic constraints and localization and may provide additional control over many-body localized phases in the time domain.
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Affiliation(s)
- Karl Royen
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
| | - Suman Mondal
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
| | - Frank Pollmann
- Physics Department, TUM School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
| | - Fabian Heidrich-Meisner
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, D-37077 Göttingen, Germany
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6
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Sinha S, Ray S, Sinha S. Classical route to ergodicity and scarring in collective quantum systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:163001. [PMID: 38190726 DOI: 10.1088/1361-648x/ad1bf5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 01/08/2024] [Indexed: 01/10/2024]
Abstract
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.
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Affiliation(s)
- Sudip Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
| | - Sayak Ray
- Physikalisches Institut, Universität Bonn, Nußallee 12, 53115 Bonn, Germany
| | - Subhasis Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
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7
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Krajnik Ž, Schmidt J, Ilievski E, Prosen T. Dynamical Criticality of Magnetization Transfer in Integrable Spin Chains. PHYSICAL REVIEW LETTERS 2024; 132:017101. [PMID: 38242668 DOI: 10.1103/physrevlett.132.017101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 11/04/2023] [Accepted: 11/30/2023] [Indexed: 01/21/2024]
Abstract
Recent studies have found that fluctuations of magnetization transfer in integrable spin chains violate the central limit property. Here, we revisit the problem of anomalous counting statistics in the Landau-Lifshitz field theory by specializing to two distinct anomalous regimes featuring a dynamical critical point. By performing optimized numerical simulations using an integrable space-time discretization, we extract the algebraic growth exponents of time-dependent cumulants which attain their threshold values. The distinctly non-Gaussian statistics of magnetization transfer in the easy-axis regime is found to converge toward the universal distribution of charged single-file systems. At the isotropic point, we infer a weakly non-Gaussian distribution, corroborating the view that superdiffusive spin transport in integrable spin chains does not belong to any known dynamical universality class.
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Affiliation(s)
- Žiga Krajnik
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
- CQP, Department of Physics, NYU, 726 Broadway, New York, New York 10003, USA
| | | | - Enej Ilievski
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
| | - Tomaž Prosen
- Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
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8
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Ogunnaike O, Feldmeier J, Lee JY. Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range Interactions. PHYSICAL REVIEW LETTERS 2023; 131:220403. [PMID: 38101343 DOI: 10.1103/physrevlett.131.220403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 08/30/2023] [Accepted: 10/23/2023] [Indexed: 12/17/2023]
Abstract
We identify emergent hydrodynamics governing charge transport in Brownian random time evolution with various symmetries, constraints, and ranges of interactions. This is accomplished via a mapping between the averaged dynamics and the low-energy spectrum of a Lindblad operator, which acts as an effective Hamiltonian in a doubled Hilbert space. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single-mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a general and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution.
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Affiliation(s)
- Olumakinde Ogunnaike
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Johannes Feldmeier
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jong Yeon Lee
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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9
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Wilming H, Osborne TJ, Decker KSC, Karrasch C. Reviving product states in the disordered Heisenberg chain. Nat Commun 2023; 14:5847. [PMID: 37730793 PMCID: PMC10511451 DOI: 10.1038/s41467-023-41464-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 09/01/2023] [Indexed: 09/22/2023] Open
Abstract
When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.
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Affiliation(s)
- Henrik Wilming
- Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany.
| | - Tobias J Osborne
- Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Kevin S C Decker
- Technische Universität Braunschweig, Institut für Mathematische Physik, Mendelssohnstraße 3, 38106, Braunschweig, Germany
| | - Christoph Karrasch
- Technische Universität Braunschweig, Institut für Mathematische Physik, Mendelssohnstraße 3, 38106, Braunschweig, Germany
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10
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Ribeiro AN. Ergodicity breaking, equilibration, and nonthermalization at the many-body energy-level crossing. Phys Rev E 2023; 108:024120. [PMID: 37723736 DOI: 10.1103/physreve.108.024120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 07/28/2023] [Indexed: 09/20/2023]
Abstract
This paper provides an analysis of the time evolution of a many-particle system starting out of equilibrium with its control parameter fixed at a value corresponding to a many-body energy-level crossing (degeneracy). We prove theorems concerning ergodicity, equilibration, and thermalization. For certain conditions, the occupancy of symmetrically equivalent basis states has different time-averaged probabilities. This nonergodicity remains in equilibrium. If the symmetrically equivalent states have opposite parity in relation to some physical property, then a left and right particle number imbalance averaged in time is nonzero. This imbalance does not occur for all initial basis states. In addition, the Hilbert space of the system is not fragmented; however, there is a subspace spanned by favored basis states, where the system is most likely to be found. Therefore, our results reveal what appears to be a unique mechanism for a weak eigenstates-thermalization-hypothesis breakdown, where the degenerate eigenstates can work as nonthermal eigenstates. To illustrate these findings, we consider the Hubbard Hamiltonian. In this case, ergodicity breaking produces a left and right magnetization imbalance, where the time-averaged probability of finding a spin-σ electron on one side of the crystal lattice is greater than on the other side. This imbalance is not associated with electrical charge; thus the conductance is preserved. The potential use in technology is discussed.
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Affiliation(s)
- André Neves Ribeiro
- Coordination of Physics, Federal Institute of Sergipe, Lagarto-SE 49400-975, Brazil
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11
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Zhang SY, Yuan D, Iadecola T, Xu S, Deng DL. Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States. PHYSICAL REVIEW LETTERS 2023; 131:020402. [PMID: 37505938 DOI: 10.1103/physrevlett.131.020402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Revised: 05/16/2023] [Accepted: 06/13/2023] [Indexed: 07/30/2023]
Abstract
Quantum many-body scarred systems host nonthermal excited eigenstates immersed in a sea of thermal ones. In cases where exact expressions for these special eigenstates are not known, it is computationally demanding to distinguish them from their exponentially many thermal neighbors. We propose a matrix-product-state (MPS) algorithm, dubbed DMRG-S, to extract such states at system sizes far beyond the scope of exact diagonalization. Using this technique, we obtain scarred eigenstates in Rydberg-blockaded chains of up to 80 sites and perform a finite-size scaling study to address the lingering question of the stability for the Néel state revivals in the thermodynamic limit. Our method also provides a systematic way to obtain exact MPS representations for scarred eigenstates near the target energy without a priori knowledge. In particular, we find several new scarred eigenstates with exact MPS representations in kinetically constrained spin and clock models. The combination of numerical and analytical investigations in our work provides a new methodology for future studies of quantum many-body scars.
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Affiliation(s)
- Shun-Yao Zhang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Dong Yuan
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Thomas Iadecola
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
- Ames National Laboratory, Ames, Iowa 50011, USA
| | - Shenglong Xu
- Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Shanghai Qi Zhi Institute, 41st Floor, AI Tower, No. 701 Yunjin Road, Xuhui District, Shanghai 200232, China
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12
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He X, Yousefjani R, Bayat A. Stark Localization as a Resource for Weak-Field Sensing with Super-Heisenberg Precision. PHYSICAL REVIEW LETTERS 2023; 131:010801. [PMID: 37478450 DOI: 10.1103/physrevlett.131.010801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 06/05/2023] [Indexed: 07/23/2023]
Abstract
Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function at all energy scales, a phenomenon known as Stark localization. Here, we show that Stark systems can be used as a probe for the precise measurement of gradient fields, particularly in the weak-field regime where most sensors do not operate optimally. In the extended phase, Stark probes achieve super-Heisenberg precision, which is well beyond most of the known quantum sensing schemes. In the localized phase, the precision drops in a universal way showing fast convergence to the thermodynamic limit. For single-particle probes, we show that quantum-enhanced sensitivity, with super-Heisenberg precision, can be achieved through a simple position measurement for all the eigenstates across the entire spectrum. For such probes, we have identified several critical exponents of the Stark localization transition and established their relationship. Thermal fluctuations, whose universal behavior is identified, reduce the precision from super-Heisenberg to Heisenberg, still outperforming classical sensors. Multiparticle interacting probes also achieve super-Heisenberg scaling in their extended phase, which shows even further enhancement near the transition point. Quantum-enhanced sensitivity is still achievable even when state preparation time is included in resource analysis.
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Affiliation(s)
- Xingjian He
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Rozhin Yousefjani
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Abolfazl Bayat
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
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13
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Kloss B, Halimeh JC, Lazarides A, Bar Lev Y. Absence of localization in interacting spin chains with a discrete symmetry. Nat Commun 2023; 14:3778. [PMID: 37355694 DOI: 10.1038/s41467-023-39468-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 06/08/2023] [Indexed: 06/26/2023] Open
Abstract
Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized-MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws.
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Affiliation(s)
- Benedikt Kloss
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Ave, New York, NY, 10010, USA.
| | - Jad C Halimeh
- Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333, München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799, München, Germany
| | - Achilleas Lazarides
- Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
| | - Yevgeny Bar Lev
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
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14
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Głódkowski A, Peña-Benítez F, Surówka P. Hydrodynamics of dipole-conserving fluids. Phys Rev E 2023; 107:034142. [PMID: 37072973 DOI: 10.1103/physreve.107.034142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Accepted: 03/15/2023] [Indexed: 04/20/2023]
Abstract
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations' dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.
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Affiliation(s)
- Aleksander Głódkowski
- Institute for Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Francisco Peña-Benítez
- Institute for Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
| | - Piotr Surówka
- Institute for Theoretical Physics, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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15
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Patil P, Heyl M, Alet F. Anomalous relaxation of density waves in a ring-exchange system. Phys Rev E 2023; 107:034119. [PMID: 37072977 DOI: 10.1103/physreve.107.034119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/05/2022] [Accepted: 02/27/2023] [Indexed: 04/20/2023]
Abstract
We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution. Through a detailed analysis of correlation functions of the dynamically active regions, we exhibit an unconventional transient long ranged structure formation in a direction which is featureless for the initial condition, and argue that its slow melting plays a crucial role in the slowing-down mechanism. We expect our results to be relevant also for the dynamics of quantum ring-exchange dynamics of hard-core bosons and more generally for dipole moment conserving models.
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Affiliation(s)
- Pranay Patil
- Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
| | - Markus Heyl
- Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
- Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
| | - Fabien Alet
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
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16
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Kohlert T, Scherg S, Sala P, Pollmann F, Hebbe Madhusudhana B, Bloch I, Aidelsburger M. Exploring the Regime of Fragmentation in Strongly Tilted Fermi-Hubbard Chains. PHYSICAL REVIEW LETTERS 2023; 130:010201. [PMID: 36669215 DOI: 10.1103/physrevlett.130.010201] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Revised: 09/09/2022] [Accepted: 11/17/2022] [Indexed: 06/17/2023]
Abstract
Intriguingly, quantum many-body systems may defy thermalization even without disorder. One example is so-called fragmented models, where the many-body Hilbert space fragments into dynamically disconnected subspaces that are not determined by the global symmetries of the model. In this Letter we demonstrate that the tilted one-dimensional Fermi-Hubbard model naturally realizes distinct effective Hamiltonians that are expected to support nonergodic behavior due to fragmentation, even at resonances between the tilt energy and the Hubbard on site interaction. We find that the effective description captures the observed dynamics in experimentally accessible parameter ranges of moderate tilt values. Specifically, we observe a pronounced dependence of the relaxation dynamics on the initial doublon fraction, which directly reveals the microscopic processes of the fragmented model. Our results pave the way for future studies of nonergodic behavior in higher dimensions.
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Affiliation(s)
- Thomas Kohlert
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Sebastian Scherg
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Pablo Sala
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Frank Pollmann
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Bharath Hebbe Madhusudhana
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Monika Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 Munich, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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17
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Kourehpaz M, Donsa S, Lackner F, Burgdörfer J, Březinová I. Canonical Density Matrices from Eigenstates of Mixed Systems. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1740. [PMID: 36554145 PMCID: PMC9778258 DOI: 10.3390/e24121740] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 11/01/2022] [Accepted: 11/04/2022] [Indexed: 06/17/2023]
Abstract
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.
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18
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Marino J, Eckstein M, Foster MS, Rey AM. Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:116001. [PMID: 36075190 DOI: 10.1088/1361-6633/ac906c] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Accepted: 09/08/2022] [Indexed: 06/15/2023]
Abstract
We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions,ϕ4quantum field theories, and Fermi-Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.
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Affiliation(s)
- Jamir Marino
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, United States of America
- Rice Center for Quantum Materials, Rice University, Houston, TX 77005, United States of America
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology, and Department of Physics,University of Colorado, Boulder, CO 80309, United States of America
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, United States of America
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19
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Aeppli A, Chu A, Bothwell T, Kennedy CJ, Kedar D, He P, Rey AM, Ye J. Hamiltonian engineering of spin-orbit-coupled fermions in a Wannier-Stark optical lattice clock. SCIENCE ADVANCES 2022; 8:eadc9242. [PMID: 36223457 PMCID: PMC9555777 DOI: 10.1126/sciadv.adc9242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a "magic" lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.
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Affiliation(s)
- Alexander Aeppli
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Anjun Chu
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Tobias Bothwell
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Colin J. Kennedy
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Dhruv Kedar
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Peiru He
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA
| | - Jun Ye
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
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20
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Huang B, Leung TH, Stamper-Kurn DM, Liu WV. Discrete Time Crystals Enforced by Floquet-Bloch Scars. PHYSICAL REVIEW LETTERS 2022; 129:133001. [PMID: 36206415 DOI: 10.1103/physrevlett.129.133001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2022] [Accepted: 08/29/2022] [Indexed: 06/16/2023]
Abstract
We analytically identify a new class of quantum scars protected by spatiotemporal translation symmetries, dubbed Floquet-Bloch scars. They are distinguished from previous (quasi-)static scars by a rigid spectral pairing only possible in Floquet systems, where strong interaction and drivings equalize the quasienergy corrections to all scars and maintain their spectral spacings against generic bilinear perturbations. Scars then enforce the spatial localization and rigid discrete time crystal (DTC) oscillations as verified numerically in a trimerized kagome lattice model relevant to recent cold atom experiments. Our analytical solutions offer a potential scheme to understand the mechanisms for more generic translation-invariant DTCs.
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Affiliation(s)
- Biao Huang
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Tsz-Him Leung
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Dan M Stamper-Kurn
- Department of Physics, University of California, Berkeley, California 94720, USA
- Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - W Vincent Liu
- Department of Physics and Astronomy and IQ Initiative, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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21
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Zhao H, Knolle J, Moessner R, Mintert F. Suppression of Interband Heating for Random Driving. PHYSICAL REVIEW LETTERS 2022; 129:120605. [PMID: 36179155 DOI: 10.1103/physrevlett.129.120605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 03/22/2022] [Accepted: 08/31/2022] [Indexed: 06/16/2023]
Abstract
Heating to high-lying states strongly limits the experimental observation of driving induced nonequilibrium phenomena, particularly when the drive has a broad spectrum. Here we show that, for entire families of structured random drives known as random multipolar drives, particle excitation to higher bands can be well controlled even away from a high-frequency driving regime. This opens a window for observing drive-induced phenomena in a long-lived prethermal regime in the lowest band.
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Affiliation(s)
- Hongzheng Zhao
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Johannes Knolle
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Florian Mintert
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany
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22
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Balducci F, Gambassi A, Lerose A, Scardicchio A, Vanoni C. Localization and Melting of Interfaces in the Two-Dimensional Quantum Ising Model. PHYSICAL REVIEW LETTERS 2022; 129:120601. [PMID: 36179178 DOI: 10.1103/physrevlett.129.120601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2022] [Revised: 06/10/2022] [Accepted: 08/04/2022] [Indexed: 06/16/2023]
Abstract
We study the nonequilibrium evolution of coexisting ferromagnetic domains in the two-dimensional quantum Ising model-a setup relevant in several contexts, from quantum nucleation dynamics and false-vacuum decay scenarios to recent experiments with Rydberg-atom arrays. We demonstrate that the quantum-fluctuating interface delimiting a large bubble can be studied as an effective one-dimensional system through a "holographic" mapping. For the considered model, the emergent interface excitations map to an integrable chain of fermionic particles. We discuss how this integrability is broken by geometric features of the bubbles and by corrections in inverse powers of the ferromagnetic coupling, and provide a lower bound to the timescale after which the bubble is ultimately expected to melt. Remarkably, we demonstrate that a symmetry-breaking longitudinal field gives rise to a robust ergodicity breaking in two dimensions, a phenomenon underpinned by Stark many-body localization of the emergent fermionic excitations of the interface.
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Affiliation(s)
- Federico Balducci
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
| | - Andrea Gambassi
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
| | - Alessio Lerose
- Department of Theoretical Physics, University of Geneva-Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
| | - Antonello Scardicchio
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
| | - Carlo Vanoni
- SISSA-International School for Advanced Studies, via Bonomea 265, 34136 Trieste, Italy
- INFN Sezione di Trieste-Via Valerio 2, 34127 Trieste, Italy
- The Abdus Salam ICTP-Strada Costiera 11, 34151 Trieste, Italy
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23
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Yoshinaga A, Hakoshima H, Imoto T, Matsuzaki Y, Hamazaki R. Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field. PHYSICAL REVIEW LETTERS 2022; 129:090602. [PMID: 36083664 DOI: 10.1103/physrevlett.129.090602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Revised: 04/10/2022] [Accepted: 08/05/2022] [Indexed: 06/15/2023]
Abstract
The transverse-field Ising model is one of the fundamental models in quantum many-body systems, yet a full understanding of its dynamics remains elusive in higher than one dimension. Here, we show for the first time the breakdown of ergodicity in d-dimensional Ising models with a weak transverse field in a prethermal regime. We demonstrate that novel Hilbert-space fragmentation occurs in the effective nonintegrable model with d≥2 as a consequence of only one emergent global conservation law of the domain wall number. Our results indicate nontrivial initial-state dependence for nonequilibrium dynamics of the Ising models with a weak transverse field.
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Affiliation(s)
- Atsuki Yoshinaga
- Department of Physics, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8574, Japan
- Research Center for Emerging Computing Technologies, National institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
| | - Hideaki Hakoshima
- Research Center for Emerging Computing Technologies, National institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka 560-0043, Japan
| | - Takashi Imoto
- Research Center for Emerging Computing Technologies, National institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
| | - Yuichiro Matsuzaki
- Research Center for Emerging Computing Technologies, National institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
| | - Ryusuke Hamazaki
- Nonequilibrium Quantum Statistical Mechanics RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR), RIKEN iTHEMS, Wako, Saitama 351-0198, Japan
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24
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Šuntajs J, Vidmar L. Ergodicity Breaking Transition in Zero Dimensions. PHYSICAL REVIEW LETTERS 2022; 129:060602. [PMID: 36018665 DOI: 10.1103/physrevlett.129.060602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 07/11/2022] [Indexed: 06/15/2023]
Abstract
It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here, we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon tuning the coupling between an ergodic quantum dot and distant particles with spin-1/2. The model is effectively zero dimensional; however, a variant of the model was proposed by De Roeck and Huveneers to describe the avalanche mechanism of ergodicity breaking transition in one-dimensional disordered spin chains. We show that exact numerical results based on the spectral form factor calculation accurately agree with theoretical predictions, and hence unambiguously confirm existence of the ergodicity breaking transition in this model. We benchmark specific properties that represent hallmarks of the ergodicity breaking transition in finite systems.
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Affiliation(s)
- Jan Šuntajs
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia and Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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25
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Moudgalya S, Bernevig BA, Regnault N. Quantum many-body scars and Hilbert space fragmentation: a review of exact results. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:086501. [PMID: 35617909 DOI: 10.1088/1361-6633/ac73a0] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck-Kennedy-Lieb-Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.
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Affiliation(s)
- Sanjay Moudgalya
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, United States of America
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, United States of America
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ 08544, United States of America
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - Nicolas Regnault
- Department of Physics, Princeton University, Princeton, NJ 08544, United States of America
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, 75005 Paris, France
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26
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De Vriendt X, Van Hende D, De Baerdemacker S, Bultinck P, Acke G. Uncovering phase transitions that underpin the flat-planes in the tilted Hubbard model using subsystems and entanglement measures. J Chem Phys 2022; 156:244115. [DOI: 10.1063/5.0092153] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The failure of many approximate electronic structure methods can be traced to their erroneous description of fractional charge and spin redistributions in the asymptotic limit toward infinity, where violations of the flat-plane conditions lead to delocalization and static correlation errors. Although the energetic consequences of the flat-planes are known, the underlying quantum phase transitions that occur when (spin)charge is redistributed have not been characterized. In this study, we use open subsystems to redistribute (spin)charges in the tilted Hubbard model by imposing suitable Lagrange constraints on the Hamiltonian. We computationally recover the flat-plane conditions and quantify the underlying quantum phase transitions using quantum entanglement measures. The resulting entanglement patterns quantify the phase transition that gives rise to the flat-plane conditions and quantify the complexity required to accurately describe charge redistributions in strongly correlated systems. Our study indicates that entanglement patterns can uncover those phase transitions that have to be modeled accurately if the delocalization and static correlation errors of approximate methods are to be reduced.
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Affiliation(s)
- Xeno De Vriendt
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Daria Van Hende
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Stijn De Baerdemacker
- Department of Chemistry, University of New Brunswick, 30 Dineen Drive, Fredericton, New Brunswick E3B 5A3, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
| | - Guillaume Acke
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 (S3), B-9000 Gent, Belgium
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27
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Joshi MK, Kranzl F, Schuckert A, Lovas I, Maier C, Blatt R, Knap M, Roos CF. Observing emergent hydrodynamics in a long-range quantum magnet. Science 2022; 376:720-724. [PMID: 35549407 DOI: 10.1126/science.abk2400] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Identifying universal properties of nonequilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. We experimentally probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain. By measuring space-time-resolved correlation functions in an infinite temperature state, we observed a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by Lévy flights. We extracted the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of nonequilibrium states of quantum matter.
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Affiliation(s)
- M K Joshi
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - F Kranzl
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria.,Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - A Schuckert
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - I Lovas
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - C Maier
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria.,AQT, Technikerstraße 17, 6020 Innsbruck, Austria
| | - R Blatt
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria.,Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
| | - M Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - C F Roos
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21a, 6020 Innsbruck, Austria.,Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
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28
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Hart O, Lucas A, Nandkishore R. Hidden quasiconservation laws in fracton hydrodynamics. Phys Rev E 2022; 105:044103. [PMID: 35590640 DOI: 10.1103/physreve.105.044103] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 02/08/2022] [Indexed: 06/15/2023]
Abstract
We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden quasiconservation laws, in which certain higher multipole moments can only decay due to dangerously irrelevant corrections to hydrodynamics. We present two simple examples of this phenomenon. First, an isotropic dipole-conserving fluid in the infinite plane conserves an infinite number of harmonic multipole charges within linear response; we calculate the decay or growth of these charges due to dangerously irrelevant nonlinearities. Second, we consider a model with xy and x^{2}-y^{2} quadrupole conservation, in addition to dipole conservation, which is described by isotropic fourth-order subdiffusion, yet has dangerously irrelevant sixth-order corrections necessary to relax the harmonic multipole charges. We confirm our predictions for the anomalously slow decay of the harmonic conserved charges in each setting by using numerical simulations, both of the nonlinear hydrodynamic differential equations, and in quantum automaton circuits on a square lattice.
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Affiliation(s)
- Oliver Hart
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Andrew Lucas
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Rahul Nandkishore
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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Zohar E. Quantum simulation of lattice gauge theories in more than one space dimension-requirements, challenges and methods. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210069. [PMID: 34923840 PMCID: PMC8886423 DOI: 10.1098/rsta.2021.0069] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/18/2021] [Indexed: 05/17/2023]
Abstract
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on [Formula: see text] dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways. This article is part of the theme issue 'Quantum technologies in particle physics'.
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Affiliation(s)
- Erez Zohar
- Racah Institute of Physics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
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30
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Li WH, Deng X, Santos L. Hilbert Space Shattering and Disorder-Free Localization in Polar Lattice Gases. PHYSICAL REVIEW LETTERS 2021; 127:260601. [PMID: 35029478 DOI: 10.1103/physrevlett.127.260601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 10/18/2021] [Accepted: 11/30/2021] [Indexed: 06/14/2023]
Abstract
Emerging dynamical constraints resulting from intersite interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the 1/r^{3} tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body localization is within reach of future experiments with magnetic atoms and polar molecules.
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Affiliation(s)
- Wei-Han Li
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - Xiaolong Deng
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
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31
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Guo Q, Cheng C, Li H, Xu S, Zhang P, Wang Z, Song C, Liu W, Ren W, Dong H, Mondaini R, Wang H. Stark Many-Body Localization on a Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2021; 127:240502. [PMID: 34951777 DOI: 10.1103/physrevlett.127.240502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
Quantum emulators, owing to their large degree of tunability and control, allow the observation of fine aspects of closed quantum many-body systems, as either the regime where thermalization takes place or when it is halted by the presence of disorder. The latter, dubbed many-body localization (MBL) phenomenon, describes the nonergodic behavior that is dynamically identified by the preservation of local information and slow entanglement growth. Here, we provide a precise observation of this same phenomenology in the case where the quenched on-site energy landscape is not disordered, but rather linearly varied, emulating the Stark MBL. To this end, we construct a quantum device composed of 29 functional superconducting qubits, faithfully reproducing the relaxation dynamics of a nonintegrable spin model. At large Stark potentials, local observables display periodic Bloch oscillations, a manifesting characteristic of the fragmentation of the Hilbert space in sectors that conserve dipole moments. The flexible programmability of our quantum emulator highlights its potential in helping the understanding of nontrivial quantum many-body problems, in direct complement to simulations in classical computers.
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Affiliation(s)
- Qiujiang Guo
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chen Cheng
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
- Beijing Computational Science Research Center, Beijing 100094, China
| | - Hekang Li
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Shibo Xu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Pengfei Zhang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhen Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Chao Song
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wuxin Liu
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Wenhui Ren
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Hang Dong
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Rubem Mondaini
- Beijing Computational Science Research Center, Beijing 100094, China
| | - H Wang
- Department of Physics and Hangzhou Innovation Center, Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
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32
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Feldmeier J, Knap M. Critically Slow Operator Dynamics in Constrained Many-Body Systems. PHYSICAL REVIEW LETTERS 2021; 127:235301. [PMID: 34936795 DOI: 10.1103/physrevlett.127.235301] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
The far-from-equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the ballistic spreading of initially local operators. Here, we show that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we study operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton chain. We identify a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase. This critical point is tied to an underlying localization transition and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We support our arguments numerically using classically simulable automaton circuits.
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Affiliation(s)
- Johannes Feldmeier
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D-80799 München, Germany
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Singh H, Ware BA, Vasseur R, Friedman AJ. Subdiffusion and Many-Body Quantum Chaos with Kinetic Constraints. PHYSICAL REVIEW LETTERS 2021; 127:230602. [PMID: 34936767 DOI: 10.1103/physrevlett.127.230602] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic timescales are given by the inverse gap of an effective Hamiltonian-or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, t_{Th}, determined by the spectral form factor, to transport properties and linear-response correlators. Using tensor network methods, we determine the dynamical exponent z for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with "Fredkin" constraints exhibit anomalous transport with dynamical exponent z≃8/3.
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Affiliation(s)
- Hansveer Singh
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Brayden A Ware
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Aaron J Friedman
- Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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Observation of Stark many-body localization without disorder. Nature 2021; 599:393-398. [PMID: 34789908 PMCID: PMC9747247 DOI: 10.1038/s41586-021-03988-0] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 09/01/2021] [Indexed: 02/08/2023]
Abstract
Thermalization is a ubiquitous process of statistical physics, in which a physical system reaches an equilibrium state that is defined by a few global properties such as temperature. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails1. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state2,3. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a spatially increasing field-but no disorder-can also exhibit MBL4, resulting in 'Stark MBL'5. Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Furthermore, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and non-thermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.
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35
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Zhao H, Smith A, Mintert F, Knolle J. Orthogonal Quantum Many-Body Scars. PHYSICAL REVIEW LETTERS 2021; 127:150601. [PMID: 34678002 DOI: 10.1103/physrevlett.127.150601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 09/16/2021] [Indexed: 06/13/2023]
Abstract
Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.
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Affiliation(s)
- Hongzheng Zhao
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Adam Smith
- School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Florian Mintert
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Johannes Knolle
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
- Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), 80799 Munich, Germany
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