Effective time reversal and echo dynamics in the transverse field Ising model

TL;DR

This paper investigates the reversibility of dynamics in the transverse field Ising model, proposing a new measure based on echo peak decay and exploring how different protocols affect irreversibility.

Contribution

It introduces a novel definition of irreversibility in quantum many-body systems and analyzes how various protocols influence the reversibility of the Ising model's dynamics.

Findings

Echo peak heights decay algebraically under certain protocols

Some protocols result in persistent echo peaks indicating reversibility

The study links protocol choice to reversibility in quantum dynamics

Abstract

The question of thermalisation in closed quantum many-body systems has received a lot of attention in the past few years. An intimately related question is whether a closed quantum system shows irreversible dynamics. However, irreversibility and what we actually mean by this in a quantum many-body system with unitary dynamics has been explored very little. In this work we investigate the dynamics of the Ising model in a transverse magnetic field involving an imperfect effective time reversal. We propose a definition of irreversibility based on the echo peak decay of observables. Inducing the effective time reversal by different protocols we find algebraic decay of the echo peak heights or an ever persisting echo peak indicating that the dynamics in this model is well reversible.