Complete Generalized Gibbs Ensemble in an interacting Theory

TL;DR

This paper constructs a complete generalized Gibbs ensemble for the spin-1/2 Heisenberg chain, incorporating quasi-local charges to accurately predict the stationary state after a quantum quench.

Contribution

It explicitly constructs a complete GGE for the Heisenberg chain, resolving a long-standing problem by including quasi-local charges for exact steady state description.

Findings

Successfully reproduces the exact post-quench steady state.

Introduces a method that generalizes to other integrable models.

Validates the GGE with the Neel quench example.

Abstract

In integrable many-particle systems, it is widely believed that the stationary state reached at late times after a quantum quench can be described by a generalized Gibbs ensemble (GGE) constructed from their extensive number of conserved charges. A crucial issue is then to identify a complete set of these charges, enabling the GGE to provide exact steady state predictions. Here we solve this long-standing problem for the case of the spin-1/2 Heisenberg chain by explicitly constructing a GGE which uniquely fixes the macrostate describing the stationary behaviour after a general quantum quench. A crucial ingredient in our method, which readily generalizes to other integrable models, are recently discovered quasi-local charges. As a test, we reproduce the exact post-quench steady state of the Neel quench problem obtained previously by means of the Quench Action method.