Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions

TL;DR

This paper provides an exact solution for the steady state of an anisotropic Heisenberg chain after a quench, revealing limitations of the generalized Gibbs ensemble in predicting the system's equilibrium properties.

Contribution

It introduces an exact analytical description of the postquench steady state in an integrable spin chain, highlighting the failure of the generalized Gibbs ensemble to accurately predict observables.

Findings

Exact steady state derived using the quench action method

GGE fails to reproduce the exact postquench state

Numerical evidence supports the discrepancy between GGE predictions and actual steady state

Abstract

We study quenches in integrable spin-1/2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit.