The generalized Gibbs ensemble for Heisenberg spin chains

Abstract

We consider the Generalized Gibbs Ensemble (GGE) in the context of global quantum quenches in XXZ Heisenberg spin chains. Embedding the GGE into the Quantum Transfer Matrix formalism we develop an iterative procedure to fix the Lagrange-multipliers and to calculate predictions for the long-time limit of short-range correlators. The main idea is to consider truncated GGE's with only a finite number of charges and to investigate the convergence of the numerical results as the truncation level is increased. As an example we consider a quantum quench situation where the system is initially prepared in the Néel state and then evolves with an XXZ Hamiltonian with anisotropy ∆ > 1. We provide predictions for short range correlators and gather numerical evidence that the iterative procedure indeed converges. The results show that the system retains memory of the initial condition, and there are clear differences between the numerical values of the correlators as calculated from the purely thermal and the Generalized Gibbs ensembles.

Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems

“…In the present work we have studied quenches between different integrable models, including interacting ones [71][72][73], or between an integrable and a chaotic Hamiltonian. These scenarios have been much less explored.…”

Entanglement prethermalization in the Tomonaga-Luttinger model

“…, (34) because it is known that integrable systems relax to the GGE [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Here, the parameters {λ k↑↓ } are determined by the initial values of the conserved quantities…”

Stationary entanglement entropies following an interaction quench in 1D Bose gas

“…This connection is in fact rather natural: long time after a quench, the reduced density matrix of a subsystem is commonly accepted to be the one of the mixed state compatible with all the local integrals of motion, i.e. a generalized Gibbs ensemble (GGE) for an integrable system [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] and a thermal ensemble for a generic system [39,40,41,42,43,44,45,46], see also Ref. [47] for a review.…”