Nontrivial damping of magnetization currents in perturbed spin chains

TL;DR

This paper investigates how perturbations affect the damping of magnetization currents in a quantum spin chain, revealing nontrivial damping behavior and providing a perturbative understanding of these effects.

Contribution

It demonstrates that magnetization current damping in a perturbed spin chain is nontrivial and introduces a modified autocorrelation function that exhibits simple damping, supported by numerical and analytical methods.

Findings

Standard autocorrelation function shows nontrivial damping.

Modified autocorrelation function exhibits simple damping.

Results align with previous findings in Hubbard chains.

Abstract

Since perturbations are omnipresent in physics, understanding their impact on the dynamics of quantum many-body systems is a vitally important but notoriously difficult question. On the one hand, random-matrix and typicality arguments suggest a rather simple damping in the overwhelming majority of cases, e.g., exponential damping according to Fermi's Golden Rule. On the other hand, counterexamples are known to exist, and it remains unclear how frequent and under which conditions such counterexamples appear. In our work, we consider the spin-1/2 XXZ chain as a paradigmatic example of a quantum many-body system and study the dynamics of the magnetization current in the easy-axis regime. Using numerical simulations based on dynamical quantum typicality, we show that the standard autocorrelation function is damped in a nontrivial way and that only a modified version of this function is damped in a simple manner. Employing projection-operator techniques in addition, we demonstrate that both, the nontrivial and simple damping relation can be understood on perturbative grounds. Our results are in agreement with earlier findings for the particle current in the Hubbard chain.