Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Relaxation and generalized Gibbs ensemble after a quench of hard-core bosons in a power-law quasiperiodic potential

Zejing Wang, Xiaohui Wang

Published Apr 1, 2026• 0 citations
Publisher

Abstract

Abstract We study the relaxation dynamics and statistical properties of hard-core bosons in a one-dimensional quasiperiodic lattice with a power-law potential following a quantum quench. Through numerical simulation of the time evolution of various one-body observables, including the on-site density, the momentum distribution, and natural orbital occupations, we find that these observables relax to non-thermal steady states. The temporal fluctuations around these steady values vanish in the thermodynamic limit. Moreover, the long-time statistics of all observables are precisely captured by a generalized Gibbs ensemble. This result confirms that generalized thermalization remains valid even in systems featuring mobility edges, where extended and localized single-particle states coexist. Our findings offer a quantitative basis for future experiments on generalized thermalization using quantum simulators with tunable mobility edges.

DOI
10.1088/1742-6596/3213/1/012009

Related papers

Quenches in a quasidisordered integrable lattice system: Dynamics and statistical description of observables after relaxation

Christian Gramsch, Marcos Rigol

We study the dynamics and the resulting state after relaxation in a quasidisordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a quasiperiodic potential whose strength is abruptly changed to take the system out of equilibrium. In the delocalized regime, we find that the relaxation dynamics of one-body observables, such as the density, the momentum distribution function, and the occupation of the natural orbitals, follow, to a good approximation, power laws. In that regime, we also show that the observables after relaxation can be described by the generalized Gibbs ensemble, while such a description fails for the momentum distribution and the natural orbital occupations in the presence of localization. At the critical point, the relaxation dynamics is found to be slower than in the delocalized phase.

arXiv:1206.3570•Physical Review A•Nov 16, 2012•99 citations

Nonequilibrium quench dynamics of hard-core bosons in quasiperiodic lattices

Xiaohui Wang, Peiqing Tong

Abstract The nonequilibrium dynamics of hard-core bosons (HCBs) in Fibonacci and generalized Fibonacci lattices following a sudden quench are studied in this paper. We numerically calculate the time evolution of one-body observables, such as the on-site density, the momentum distribution function and the occupation of the natural orbitals. It is found that in Fibonacci lattices the observables relax to time-independent values after the quenches. Moreover, after relaxation the generalized Gibbs ensemble (GGE) provides a good description for the on-site density, while GGE fails to describe the momentum distribution function and the occupation of the natural orbitals. These results are similar to those of HCBs in the localized regime of the Aubry-André model. We also studied the dynamics of HCBs in generalized Fibonacci lattices, and found that the relaxation dynamics and the resulting states after relaxation are similar to those in Fibonacci lattices.

Journal of Statistical Mechanics Theory and Experiment•Nov 1, 2017•4 citations

Single-particle and many-body analyses of a quasiperiodic integrable system after a quench

Kai He, Léa Ferreira dos Santos, Tod M. Wright +1 more

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andr\'e model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.

arXiv:1304.2778•Physical Review A•Jun 26, 2013•54 citations

Generalized Thermalization in an Integrable Lattice System

Amy Cassidy, Charles W. Clark, Marcos Rigol

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (≈10(10) eigenstates) validate our approach.

arXiv:1008.4794•Physical Review Letters•Apr 8, 2011•351 citations

Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons

Marcos Rigol, Vanja Dunjko, Vladimir Yurovsky +1 more

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].

arXiv:cond-mat/0604476•Physical Review Letters•Feb 1, 2007•1,571 citations

Nonequilibrium Dynamics of One-Dimensional Hard-Core Anyons Following a Quench: Complete Relaxation of One-Body Observables

Tod M. Wright, Marcos Rigol, Matthew J. Davis +1 more

We demonstrate the role of interactions in driving the relaxation of an isolated integrable quantum system following a sudden quench. We consider a family of integrable hard-core lattice anyon models that continuously interpolates between noninteracting spinless fermions and strongly interacting hard-core bosons. A generalized Jordan-Wigner transformation maps the entire family to noninteracting fermions. We find that, aside from the singular free-fermion limit, the entire single-particle density matrix and, therefore, all one-body observables relax to the predictions of the generalized Gibbs ensemble (GGE). This demonstrates that, in the presence of interactions, correlations between particles in the many-body wave function provide the effective dissipation required to drive the relaxation of all one-body observables to the GGE. This relaxation does not depend on translational invariance or the tracing out of any spatial domain of the system.

arXiv:1312.4657•Physical Review Letters•Jul 29, 2014•77 citations
Abstract We study the relaxation dynamics and statistical properties of hard-core bosons in a one-dimensional quasiperiodic lattice with a power-law potential following a quantum quench. Through numerical simulation of the time evolution of various one-body observables, including the on-site density, the momentum distribution, and natural orbital occupations, we find that these observables relax to non-thermal steady states. The temporal fluctuations around these steady values vanish in the thermodynamic limit. Moreover, the long-time statistics of all observables are precisely captured by a generalized Gibbs ensemble. This result confirms that generalized thermalization remains valid even in systems featuring mobility edges, where extended and localized single-particle states coexist. Our findings offer a quantitative basis for future experiments on generalized thermalization using quantum simulators with tunable mobility edges.
We study the dynamics and the resulting state after relaxation in a quasidisordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a quasiperiodic potential whose strength is abruptly changed to take the system out of equilibrium. In the delocalized regime, we find that the relaxation dynamics of one-body observables, such as the density, the momentum distribution function, and the occupation of the natural orbitals, follow, to a good approximation, power laws. In that regime, we also show that the observables after relaxation can be described by the generalized Gibbs ensemble, while such a description fails for the momentum distribution and the natural orbital occupations in the presence of localization. At the critical point, the relaxation dynamics is found to be slower than in the delocalized phase.
Abstract The nonequilibrium dynamics of hard-core bosons (HCBs) in Fibonacci and generalized Fibonacci lattices following a sudden quench are studied in this paper. We numerically calculate the time evolution of one-body observables, such as the on-site density, the momentum distribution function and the occupation of the natural orbitals. It is found that in Fibonacci lattices the observables relax to time-independent values after the quenches. Moreover, after relaxation the generalized Gibbs ensemble (GGE) provides a good description for the on-site density, while GGE fails to describe the momentum distribution function and the occupation of the natural orbitals. These results are similar to those of HCBs in the localized regime of the Aubry-André model. We also studied the dynamics of HCBs in generalized Fibonacci lattices, and found that the relaxation dynamics and the resulting states after relaxation are similar to those in Fibonacci lattices.
In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andr\'e model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.
After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (≈10(10) eigenstates) validate our approach.
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].
We demonstrate the role of interactions in driving the relaxation of an isolated integrable quantum system following a sudden quench. We consider a family of integrable hard-core lattice anyon models that continuously interpolates between noninteracting spinless fermions and strongly interacting hard-core bosons. A generalized Jordan-Wigner transformation maps the entire family to noninteracting fermions. We find that, aside from the singular free-fermion limit, the entire single-particle density matrix and, therefore, all one-body observables relax to the predictions of the generalized Gibbs ensemble (GGE). This demonstrates that, in the presence of interactions, correlations between particles in the many-body wave function provide the effective dissipation required to drive the relaxation of all one-body observables to the GGE. This relaxation does not depend on translational invariance or the tracing out of any spatial domain of the system.