A test of the g-ology model for one-dimensional interacting Fermi systems

TL;DR

This paper tests the g-ology model's predictions for the specific heat of one-dimensional interacting Fermi systems, confirming that it reproduces bosonization results and can incorporate anomalous terms via renormalized spin velocity.

Contribution

It demonstrates the equivalence of g-ology and bosonization results for specific heat, including anomalous terms, using numerical solutions of the Bethe-ansatz equations.

Findings

G-ology reproduces bosonization predictions for C(T).

Anomalous terms are incorporated into a renormalized spin velocity.

Results are validated through Bethe-ansatz numerical solutions.

Abstract

Bosonization predicts that the specific heat, C(T), of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing T. We verify whether this result is reproduced in the g-ology model. Of specific interest are the anomalous terms in C(T) that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for C(T) obtained within the g-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.