Generalized Gibbs Ensemble for Heisenberg Spin Chains

TL;DR

This paper develops a method to compute long-time correlators in XXZ Heisenberg spin chains after a quantum quench by using a truncated Generalized Gibbs Ensemble within the Quantum Transfer Matrix formalism, demonstrating convergence and initial state memory effects.

Contribution

It introduces an iterative procedure to determine Lagrange multipliers for the GGE in spin chains, enabling accurate predictions of long-time correlators after quenches.

Findings

The iterative method converges as the number of charges increases.

The system retains memory of the initial Ne9el state.

Differences are observed between thermal and GGE predictions.

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 N\'eel state and then evolves with an XXZ Hamiltonian with anisotropy Delta>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.