Quench action approach for releasing the N\'eel state into the spin-1/2 XXZ chain

TL;DR

This paper analyzes the steady state after a quantum quench from the Ne9el state to the XXZ spin chain, comparing the generalized Gibbs ensemble and quench action methods, and providing exact analytical descriptions of the postquench state.

Contribution

It offers the first exact Bethe root density description of the Ne9el-to-XXZ quench steady state and systematically compares two theoretical approaches.

Findings

Exact Bethe root densities for the Ne9el-to-XXZ quench

Analytical differences between GGE and quench action predictions

Validation of quench action assumptions for isotropic case

Abstract

The steady state after a quantum quench from the N\'eel state to the anisotropic Heisenberg model for spin chains is investigated. Two methods that aim to describe the postquench non-thermal equilibrium, the generalized Gibbs ensemble and the quench action approach, are discussed and contrasted. Using the recent implementation of the quench action approach for this N\'eel-to-XXZ quench, we obtain an exact description of the steady state in terms of Bethe root densities, for which we give explicit analytical expressions. Furthermore, by developing a systematic small-quench expansion around the antiferromagnetic Ising limit, we analytically investigate the differences between the predictions of the two methods in terms of densities and postquench equilibrium expectation values of local physical observables. Finally, we discuss the details of the quench action solution for the quench to the isotropic Heisenberg spin chain. For this case we validate the underlying assumptions of the quench action approach by studying the large-system-size behavior of the overlaps between Bethe states and the N\'eel state.