Scaling limit of the one-dimensional attractive Hubbard model: The half-filled band case

TL;DR

This paper analyzes the scaling limit of the half-filled one-dimensional attractive Hubbard model, revealing its connection to conformal field theory and confirming results with perturbative calculations.

Contribution

It provides a detailed analysis of the Bethe Ansatz equations for the Hubbard model, identifying the spectrum's structure and its relation to conformal field theory.

Findings

Massless sector corresponds to a c=1 conformal field

Finite size corrections match perturbative SU(2) chiral Gross-Neveu model

Spectrum decouples into three sets of Bethe Ansatz equations

Abstract

The scaling limit of the higher level Bethe Ansatz (HLBA) equations for a macroscopically half-filled Hubbard chain is considered. These equations practically decouple into three disjoint sets which are again of the BA type, and correspond to the secular equations of three different kinds of dressed particles (one massive and two massless). The finite size corrections and the fine structure of the spectrum show that the massless sector corresponds to a conformal field with central charge c=1 and Gaussian anomalous dimensions. The zero temperature free energy is also calculated and is found to be in perfect agreement with the results of a perturbative calculation in the SU(2) chiral Gross-Neveu (CGN) model.