Canonical Drude weight for non-integrable quantum spin chains

TL;DR

This paper proves the equivalence of Euclidean and canonical Drude weights at zero temperature in quantum spin chains using rigorous renormalization group methods, clarifying the transport properties in both integrable and non-integrable models.

Contribution

It establishes the first rigorous proof of the equivalence between Euclidean and canonical Drude weights at zero temperature for non-integrable quantum spin chains.

Findings

Proved the equivalence of Euclidean and canonical Drude weights at zero temperature.

Applied rigorous renormalization group, Ward identities, and complex analysis techniques.

Confirmed universality results for transport properties in quantum spin chains.

Abstract

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably the proof works for both for integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.