Drude Weight at Finite Temperatures for Some Non-Integrable Quantum Systems in One Dimension

TL;DR

This paper demonstrates that certain one-dimensional quantum liquids maintain a non-zero Drude weight at finite temperatures despite non-integrability, using conformal perturbation theory and providing an accurate low-temperature formula.

Contribution

It introduces a method to compute the finite-temperature Drude weight in non-integrable 1D quantum systems, extending understanding beyond integrable models.

Findings

Non-zero Drude weight persists at finite temperatures in some non-integrable systems.

Derived an asymptotically exact low-temperature formula for the Drude weight.

Results agree well with recent numerical data for Heisenberg XXZ chains.

Abstract

Using conformal perturbation theory, we show that for some classes of the one-dimensional quantum liquids that possess the Luttinger liquid fixed point in the low energy limit, the Drude weight at finite temperatures is non-vanishing, even when the system is {\it non-integrable} and the total current is not conserved. We also obtain the asymptotically exact low-temperature formula of the Drude weight for Heisenberg XXZ spin chains, which agrees quite well with recent numerical data.