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

TL;DR

This paper analyzes the scaling limit of a one-dimensional attractive Hubbard model away from half-filling, revealing a structure similar to the half-filled case but with distinct massless excitations, and connects it to the SU(2) Gross-Neveu model.

Contribution

It constructs the continuum limit of the non-half-filled attractive Hubbard chain and identifies its relation to the SU(2) Gross-Neveu model, highlighting differences in the massless sector.

Findings

The limiting model has both massive and massless sectors.

The massive sector resembles the half-filled case and the CGN model.

The massless sector exhibits a tower structure with c=1 and SU(2)xSU(2) symmetry.

Abstract

The scaling limit of the less than half filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth in a such way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find, that similarly to the half filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c=1 and SU(2)xSU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory.