A partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

TL;DR

This paper develops an approximate partition functional for the infinite-dimensional Hubbard model, capturing key thermodynamic properties, including the Kondo anomaly and Hubbard pseudo-gap, with results consistent with known limits.

Contribution

It introduces a new approximate functional that includes the Falicov-Kimball model as a special case and remains exact in certain limits, explicitly maintaining spin-symmetry.

Findings

Satisfies Luttinger theorem at zero temperature

Reveals a Kondo-type anomaly at a characteristic temperature T*

Shows resistivity behavior consistent with experimental observations

Abstract

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin-symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature $T^\star$. We attribute this anomaly to the appearance of the Hubbard pseudo-gap. The specific heat also shows a peak near $T^\star$. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around $T^\star$ and has a rough linear temperature dependence above $T^\star$.