Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

TL;DR

This paper develops finite temperature strong coupling expansions for the SU(N) Hubbard model, enabling analysis of thermodynamic properties across various temperatures and fillings, especially near one particle per site.

Contribution

The authors introduce a novel strong coupling expansion framework for the SU(N) Hubbard model at finite temperatures, applicable for arbitrary fillings and converging over a broad temperature range.

Findings

Expansions converge for U larger than or comparable to bandwidth.

At low temperatures, expansions relate to SU(N) Heisenberg and t-J models.

Plateau in entropy indicates onset of strong correlations.

Abstract

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $\beta t$, $w=\exp{(-\beta U)}$ and ${1\over \beta U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for $U$ larger than or of order the Bandwidth, the expansions converge over a wide temperature range $t^2/U \ \lesssim \ T \ \lesssim \ 10 U$. By taking the limit $w\to 0$, valid at temperatures much less than $U$, the expansions turn into a high temperature expansion for a dressed SU(N) Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges and ring exchanges known from the $T=0$ perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the $w\to 0$ limit corresponds to an effective $t-J$ model. The onset of strong correlations can be identified by a plateau-like behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter $\delta=1-n$, the deviation from one particle per site, where the leading $\beta t$ dependent terms correspond to holes sloshing around in a disordered SU(N) background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.