The half-filled Hubbard model in the pair approximation of the Cluster Variation Method

TL;DR

This paper analyzes the half-filled Hubbard model using the pair approximation of the Cluster Variation Method, providing analytical ground state characterization and finite temperature behavior, with results aligning well with known data.

Contribution

It offers a complete analytical description of the ground state and finite temperature properties of the Hubbard model within the pair approximation, leveraging $SO(4)$ symmetry.

Findings

Analytical expressions for double occupancy and correlation functions.

Qualitative agreement with exact and numerical results in 1D.

Observation of a maximum in specific heat indicating a metal-insulator transition.

Abstract

The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions for the double occupancy and the nearest neighbor correlation functions. The finite temperature analysis is reduced to the numerical solution of only two coupled transcendental equations. The behavior of local magnetic moment, specific heat and correlation functions is given for some typical cases in one and two dimensions. We obtain good qualitative agreement with exact and numerical results in one dimension. The results for finite temperatures show a rapid evolution, with increasing temperature, from a strongly antiferromagnetic behavior to a disordered one; in the high temperature region a maximum (which has been related to a "gradual" metal--insulator transition) is found in the specific heat for very large values of the Coulomb repulsion.