Weak integrability breaking: chaos with integrability signature in coherent diffusion

TL;DR

This paper investigates how infinitesimal perturbations cause a transition from integrability to chaos in quantum many-body systems, revealing a modified diffusion behavior and the nuanced role of impurities in transport properties.

Contribution

It demonstrates that even tiny perturbations induce diffusive transport in the thermodynamic limit and uncovers a modified Matthiessen's rule in non-ballistic quantum systems.

Findings

Transport becomes diffusive at infinitesimal perturbations in the thermodynamic limit.

Diffusion constant depends on impurity density, deviating from Matthiessen's rule.

Adding impurities can sometimes enhance transport, contrary to expectations.

Abstract

We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of the inverse density, instead of to the inverse density as would follow from Matthiessen's rule. We show that Matthiessen's rule has to be modified in non-ballistic systems. Results also highlight a nontrivial role of interacting scattering on a single impurity, and that there is a regime where adding more impurities can actually increase transport.