Kubo's response theory and bosonization with a background gauge field and irrelevant perturbations

TL;DR

This paper investigates the effects of flux insertion and Umklapp perturbations on the energy spectrum and conductivity in the XXZ model using conformal field theory, highlighting discrepancies between different theoretical approaches.

Contribution

It compares two methods for evaluating the Drude weight in the XXZ model, clarifies the role of perturbation order, and computes the scaling of conductivity with system size and temperature.

Findings

Divergences in linear response contradict Bethe ansatz results.

The two approaches agree only at the free fermion point.

Conductivity scales with system size and temperature in the long-wave limit.

Abstract

Using conformal field theory calculations of the energy spectrum, within the XXZ model we investigate effects of the flux insertion and the Umklapp term. We discuss two approaches to the evaluation of the Drude weight, the first corresponding to the linear response theory and the second corresponding to the twisted boson theory with the Umklapp term. Divergences obtained in the context of the former contradict the Bethe ansatz results, with the two approaches coinciding for the free fermion point only. The origin of this discrepancy is in the different order in which the Umklapp term and the flux insertion are treated, where the marginal perturbation should be considered before the irrelevant. We calculate the scaling of the conductivity with system size and temperature in the long-wave limit.