Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain

TL;DR

This paper derives exact results for the Loschmidt echo and overlaps in the Heisenberg XXZ spin chain after quantum quenches from specific initial states, revealing insights into dynamical free energy and quantum coherence.

Contribution

It provides the first exact analytic expressions for the Loschmidt echo per site at imaginary times and overlaps for certain initial states in the XXZ chain.

Findings

Exact analytic results for Loschmidt echo per site at imaginary times.

Exact overlap per site between Néel state and ground state.

Insights into dynamical free energy in quantum quenches.

Abstract

We consider a class of global quantum quenches in the Heisenberg XXZ spin chain, where the initial states are given by products of local two-site states. The two main examples are the N\'eel state and the dimer state. We derive an exact analytic result for the "Loschmidt echo per site" at imaginary times and also consider the analytic continuation back to real times. As a by-product we obtain an exact result for the "overlap per site" between the N\'eel state and the ground state of the XXZ Hamiltonian in the massive regime.