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Singh H, Kolodrubetz MH, Gopalakrishnan S, Vasseur R. Tunable Superdiffusion in Integrable Spin Chains Using Correlated Initial States. PHYSICAL REVIEW LETTERS 2024; 132:176303. [PMID: 38728724 DOI: 10.1103/physrevlett.132.176303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Revised: 02/05/2024] [Accepted: 04/01/2024] [Indexed: 05/12/2024]
Abstract
Although integrable spin chains host only ballistically propagating particles, they can still feature diffusive charge transfer. This diffusive charge transfer originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long-range correlations lead to superdiffusive charge transfer with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and discuss how finite time and finite size effects might cause deviations.
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Affiliation(s)
- Hansveer Singh
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Michael H Kolodrubetz
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Sarang Gopalakrishnan
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Perfetto G, Carollo F, Garrahan JP, Lesanovsky I. Quantum reaction-limited reaction-diffusion dynamics of annihilation processes. Phys Rev E 2023; 108:064104. [PMID: 38243424 DOI: 10.1103/physreve.108.064104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 10/23/2023] [Indexed: 01/21/2024]
Abstract
We investigate the quantum reaction-diffusion dynamics of fermionic particles which coherently hop in a one-dimensional lattice and undergo annihilation reactions. The latter are modelled as dissipative processes which involve losses of pairs 2A→∅, triplets 3A→∅, and quadruplets 4A→∅ of neighboring particles. When considering classical particles, the corresponding decay of their density in time follows an asymptotic power-law behavior. The associated exponent in one dimension is different from the mean-field prediction whenever diffusive mixing is not too strong and spatial correlations are relevant. This specifically applies to 2A→∅, while the mean-field power-law prediction just acquires a logarithmic correction for 3A→∅ and is exact for 4A→∅. A mean-field approach is also valid, for all the three processes, when the diffusive mixing is strong, i.e., in the so-called reaction-limited regime. Here we show that the picture is different for quantum systems. We consider the quantum reaction-limited regime and we show that for all the three processes power-law behavior beyond mean field is present as a consequence of quantum coherences, which are not related to space dimensionality. The decay in 3A→∅ is further, highly intricate, since the power-law behavior therein only appears within an intermediate time window, while at long times the density decay is not power law. Our results show that emergent critical behavior in quantum dynamics has a markedly different origin, based on quantum coherences, to that applying to classical critical phenomena, which is, instead, solely determined by the relevance of spatial correlations.
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Affiliation(s)
- Gabriele Perfetto
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
| | - Federico Carollo
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Universität Tübingen, 72076 Tübingen, Germany
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Perfetto G, Carollo F, Garrahan JP, Lesanovsky I. Reaction-Limited Quantum Reaction-Diffusion Dynamics. PHYSICAL REVIEW LETTERS 2023; 130:210402. [PMID: 37295117 DOI: 10.1103/physrevlett.130.210402] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Revised: 02/03/2023] [Accepted: 04/10/2023] [Indexed: 06/12/2023]
Abstract
We consider the quantum nonequilibrium dynamics of systems where fermionic particles coherently hop on a one-dimensional lattice and are subject to dissipative processes analogous to those of classical reaction-diffusion models. Particles can either annihilate in pairs, A+A→0, or coagulate upon contact, A+A→A, and possibly also branch, A→A+A. In classical settings, the interplay between these processes and particle diffusion leads to critical dynamics as well as to absorbing-state phase transitions. Here, we analyze the impact of coherent hopping and of quantum superposition, focusing on the so-called reaction-limited regime. Here, spatial density fluctuations are quickly smoothed out due to fast hopping, which for classical systems is described by a mean-field approach. By exploiting the time-dependent generalized Gibbs ensemble method, we demonstrate that quantum coherence and destructive interference play a crucial role in these systems and are responsible for the emergence of locally protected dark states and collective behavior beyond mean field. This can manifest both at stationarity and during the relaxation dynamics. Our analytical results highlight fundamental differences between classical nonequilibrium dynamics and their quantum counterpart and show that quantum effects indeed change collective universal behavior.
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Affiliation(s)
- Gabriele Perfetto
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Federico Carollo
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Juan P Garrahan
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics, Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics, Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Singh H, Vasseur R, Gopalakrishnan S. Fredkin Staircase: An Integrable System with a Finite-Frequency Drude Peak. PHYSICAL REVIEW LETTERS 2023; 130:046001. [PMID: 36763442 DOI: 10.1103/physrevlett.130.046001] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Revised: 01/08/2023] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the dc limit, albeit with a highly non-Gaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the ac conductivity at nonzero frequency. We analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower bound the weight of this finite-frequency singularity.
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Affiliation(s)
- Hansveer Singh
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Sarang Gopalakrishnan
- Department of Physics, Pennsylvania State University, University Park Pennsylvania 16802, USA
- Department of Electrical and Computer Engineering, Princeton University, Princeton New Jersey 08544, USA
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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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Pérez-Espigares C, Marcuzzi M, Gutiérrez R, Lesanovsky I. Epidemic Dynamics in Open Quantum Spin Systems. PHYSICAL REVIEW LETTERS 2017; 119:140401. [PMID: 29053308 DOI: 10.1103/physrevlett.119.140401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2017] [Indexed: 06/07/2023]
Abstract
We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state. We show that in a two-dimensional lattice, depending on the dominance of either classical or quantum effects, the system may display a different kind of nonequilibrium phase transition. We moreover discuss the observability of our findings in laser driven Rydberg gases with particular focus on the role of long-range interactions.
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Affiliation(s)
- Carlos Pérez-Espigares
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Matteo Marcuzzi
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Ricardo Gutiérrez
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom and Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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Marcuzzi M, Minář J, Barredo D, de Léséleuc S, Labuhn H, Lahaye T, Browaeys A, Levi E, Lesanovsky I. Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder. PHYSICAL REVIEW LETTERS 2017; 118:063606. [PMID: 28234523 DOI: 10.1103/physrevlett.118.063606] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 06/06/2023]
Abstract
We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.
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Affiliation(s)
- Matteo Marcuzzi
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Jiří Minář
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Daniel Barredo
- Laboratoire Charles Fabry, Institut d'Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - Sylvain de Léséleuc
- Laboratoire Charles Fabry, Institut d'Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - Henning Labuhn
- Laboratoire Charles Fabry, Institut d'Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - Thierry Lahaye
- Laboratoire Charles Fabry, Institut d'Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - Antoine Browaeys
- Laboratoire Charles Fabry, Institut d'Optique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - Emanuele Levi
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Igor Lesanovsky
- School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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