Ballistic-to-diffusive transition in spin chains with broken integrability

TL;DR

This paper investigates how weak breaking of integrability in boundary-driven XXZ spin chains causes a transition from ballistic to diffusive transport, revealing a universal behavior near the XX limit and a transient quasi-ballistic regime influenced by interactions.

Contribution

It uncovers the universal scaling of the ballistic-to-diffusive transition controlled by scattering length and highlights the emergence of a transient quasi-ballistic regime due to interactions.

Findings

Transition controlled by scattering length $L^*\propto V^{-2}$

Universal behavior near the XX limit

Transient quasi-ballistic regime at short scales

Abstract

We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin-chain. Studying the evolution of the spin current density $\mathcal J^s$ as a function of the system size $L$, we show that, accounting for boundary effects, the transition has a non-trivial universal behavior close to the XX limit. It is controlled by the scattering length $L^*\propto V^{-2}$, where $V$ is the strength of the integrability breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient "quasi-ballistic" regime at length scales much shorter than $L^*$. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on Matrix Product Operator numerical simulations and agree with perturbative analytical calculations.