Comment on "Spin Transport properties of the quantum one-dimensional non-linear sigma model"

TL;DR

This paper critiques a recent study on spin transport in the quantum O(3) non-linear sigma model, clarifying that its results align with earlier semiclassical findings and highlighting issues with its 1/N expansion approach.

Contribution

It clarifies the consistency of recent Bethe ansatz results with semiclassical theories and critiques the validity of the 1/N expansion in describing long-time correlations.

Findings

Bethe ansatz results agree with semiclassical results

The 1/N expansion does not accurately describe long-time correlations

The critique resolves discrepancies in spin transport calculations

Abstract

In a recent preprint (cond-mat/9905415), Fujimoto has used the Bethe ansatz to compute the finite temperature, zero frequency Drude weight of spin transport in the quantum O(3) non-linear sigma model in a magnetic field $H \neq 0$. We show here that, contrary to his claims, the results are in accord with earlier semiclassical results (Sachdev and Damle, cond-mat/9610115). We also comment on his 1/N expansion, and show that it does not properly describe the long-time correlations.