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Journal of Statistical Mechanics Theory and Experiment

Nonequilibrium quench dynamics of hard-core bosons in quasiperiodic lattices

Xiaohui Wang, Peiqing Tong

Published Nov 1, 2017• 4 citations
Publisher

Abstract

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.

DOI
10.1088/1742-5468/aa9093

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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 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 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.
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.
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We develop an exact approach to study the quench dynamics of hard-core bosons initially in thermal equilibrium in one-dimensional lattices. This approach is used to study the sudden expansion of thermal states after confining potentials are switched off. We find that a dynamical fermionization of the momentum distribution occurs at all temperatures. This phenomenon is studied for low initial site occupations, for which the expansion of the cloud is self-similar. In this regime, the occupation of the natural orbitals allows one to distinguish hard-core bosons from noninteracting fermions. We also study the free expansion of initial Mott insulating domains at finite temperature and show that the emergence of off-diagonal one-body correlations is suppressed gradually with increasing temperature. Surprisingly, the melting of the Mott domain is accompanied by an effective cooling of the system. We explain this phenomenon analytically using an equilibrium description based on an emergent local Hamiltonian.