Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results

TL;DR

This paper provides exact analytical results for the Loschmidt echo in the XXZ spin-1/2 chain after a quantum quench, revealing non-analyticities associated with level crossings in the dynamical free energy.

Contribution

It introduces a novel exact method to compute the Loschmidt echo in interacting integrable models, capturing non-analyticities through excited-state Bethe ansatz equations.

Findings

Exact results for dynamical free energy in XXZ chain

Identification of non-analytic points in Loschmidt echo

Explicit numerical results for N9el state quench

Abstract

We address the computation of the Loschmidt echo in interacting integrable spin chains after a quantum quench. We focus on the massless regime of the XXZ spin-1/2 chain and present exact results for the dynamical free energy (Loschmidt echo per site) for a special class of integrable initial states. For the first time we are able to observe and describe points of non-analyticities using exact methods, by following the Loschmidt echo up to large real times. The dynamical free energy is computed as the leading eigenvalue of an appropriate Quantum Transfer Matrix, and the non-analyticities arise from the level crossings of this matrix. Our exact results are expressed in terms of "excited-state" thermodynamic Bethe ansatz equations, whose solutions involve non-trivial Riemann surfaces. By evaluating our formulas, we provide explicit numerical results for the quench from the N\'eel state, and we determine the first few non-analytic points.