Critical exponents of the degenerate Hubbard model

TL;DR

This paper analyzes the critical behavior of the ext{SU}(N) Hubbard model in one dimension, calculating excitation spectra and correlation function exponents using Bethe Ansatz, revealing how degeneracy and interactions influence critical phenomena.

Contribution

It provides the first detailed calculation of critical exponents for the ext{SU}(N) Hubbard model with arbitrary degeneracy using integrability techniques.

Findings

Critical exponents depend on system parameters via an N×N dressed charge matrix.

Correlation functions exhibit asymptotic behavior influenced by charge- and spin-density wave interactions.

The model's integrability allows for exact computation of low-lying excitation spectra.

Abstract

We study the critical behaviour of the \SUN{} generalization of the one-dimensional Hubbard model with arbitrary degeneracy $N$. Using the integrability of this model by Bethe Ansatz we are able to compute the spectrum of the low-lying excitations in a large but finite box for arbitrary values of the electron density and of the Coulomb interaction. This information is used to determine the asymptotic behaviour of correlation functions at zero temperature in the presence of external fields lifting the degeneracy. The critical exponents depend on the system parameters through a $N\times N$ dressed charge matrix implying the relevance of the interaction of charge- and spin-density waves.