Comment on ``On the Renormalization of Conductance in Tomonaga-Luttinger Liquid''

TL;DR

This paper discusses how proper inclusion of field renormalization shows conductance in Tomonaga-Luttinger liquids remains unrenormalized, even with large momentum transfer interactions, confirming Kawabata's conclusion.

Contribution

It generalizes Kawabata's result to include large momentum transfer interactions, showing they only renormalize velocity and TL parameters, not conductance.

Findings

Conductance in TL liquids is not renormalized when fields are correctly accounted for.

Irrelevant interactions only renormalize velocity and TL parameters.

Kawabata's conclusion holds generally for TL liquids.

Abstract

Recently Kawabata found that the conductance in Tomonaga-Luttinger (TL) liquids should not be renormalized if one incorporates the renormalization of applied fields correctly. This claim is generalized to include the interactions which carry the large momentum transfer. We thus find that Kawabata's conclusion holds generally for the class of TL liquids. A key observation is that such irrelevant interactions merely renormalize the velocity and the TL parameter at the massless TL fixed point.