Transport in Almost Integrable Models: Perturbed Heisenberg Chains

TL;DR

This paper investigates how small perturbations affect heat transport in nearly integrable Heisenberg chains, revealing different scaling behaviors and a new conservation law that influence thermal conductivity.

Contribution

It introduces a perturbative approach to calculate finite thermal conductivity in nearly integrable models and uncovers a new approximate conservation law affecting transport.

Findings

Interchain coupling leads to conductivity scaling as 1/J_perp^2.

Next-nearest neighbor interaction results in conductivity scaling as 1/J'^4.

A new approximate conservation law explains the enhanced conductivity scaling.

Abstract

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.