Spin conductivity in almost integrable spin chains

TL;DR

This paper investigates how breaking integrability in the spin-1/2 XXZ chain affects spin conductivity, revealing a lower bound and the role of non-local conserved operators in transport properties.

Contribution

The study constructs a non-local conserved operator responsible for finite spin Drude weight and derives a lower bound for spin conductivity in nearly integrable chains.

Findings

Finite spin conductivity bound inversely proportional to square of perturbation J'

Identification of a non-local conserved operator affecting transport

Implications for non-local conservation laws in quantum transport

Abstract

The spin conductivity in the integrable spin-1/2 XXZ-chain is known to be infinite at finite temperatures T for anisotropies -1 < Delta < 1. Perturbations which break integrability, e.g. a next-nearest neighbor coupling J', render the conductivity finite. We construct numerically a non-local conserved operator J_parallel which is responsible for the finite spin Drude weight of the integrable model and calculate its decay rate for small J'. This allows us to obtain a lower bound for the spin conductivity sigma_s >= c(T) / J'^2, where c(T) is finite for J' to 0. We discuss the implication of our result for the general question how non-local conservation laws affect transport properties.