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

Abstract

We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of βt, w = exp (−βU ) and 1 βU 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 T 10U . By taking the limit w → 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 → 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 δ = 1 − n, the deviation from one particle per site, where the leading βt 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.

On the Divergence of the Ferromagnetic Susceptibility in the SU(N) Nagaoka-Thouless Ferromagnet

“…After changing variables from fugacity to particle density ρ, one can obtain temperature dependent thermodynamic properties at various densities. For U of order or larger than the bandwidth they allow one to relate the thermodynamics of the Hubbard model at low temperatures to a generalized Heisenberg or t-J model [33][34][35][36]. The expansions simplify in the limit U → ∞, in which case many terms can be set to zero and can be used to study the problem of Nagaoka-Thouless ferromagnetism.…”