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

Abstract

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. One-dimensional (1D) quantum systems exhibit two features unfamiliar in the three-dimensional world. The first is the breakdown of the strict distinction between bosonic and fermionic particle statistics [1,2], and the second is the prospect of integrability in the presence of interactions [3]. Integrable models have been of particular interest as they can be studied using exact analytic and computational approaches to gain insights into strongly correlated quantum systems [4]. A recent surge of interest in the nonequilibrium dynamics of these systems [4][5][6][7][8] has been motivated by the failure of some quasi-1D systems in cold-atom experiments [9,10] to relax to states consistent with conventional statistical mechanics.A paradigmatic model in this realm is that of lattice hardcore bosons (HCBs), which is integrable by virtue of an exact mapping via the Jordan-Wigner transformation to a system of noninteracting spinless fermions (SFs) [11]. Rigol et al. [12] showed that, following an abrupt change of Hamiltonian parameters (quantum quench), certain single-particle properties of HCBs such as site and momentum occupations relax to stationary distributions that are not consistent with the predictions of conventional statistical ensembles but can be described by a generalized Gibbs ensemble (GGE). The GGE is obtained by maximizing the entropy subject to the constraints that the mean values of the conserved quantitieŝ I l that make the system integrable are fixed to their values in the initial state. This yields the density matrixwhere the Lagrange multipliers λ l are such that Trfρ GGEÎl g ¼ hÎ l i I , with hÁ Á Ái I denoting an expectation value taken in the initial (prequench) state of the system and the partition function Z GGE ¼ Trfexpð− P l λ lÎl Þg. The validity of the GGE for various classes of observables has now been verified for the relaxed states following quenches of HCBs in a number of distinct geometries [12][13][14][15] and in a range of other integrable systems [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, the role of interactions ...

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