Grand Canonical Partition Function for Unidimensional Systems: Application to Hubbard Model up to Order beta^3

TL;DR

This paper develops a method to compute the high-temperature expansion of the grand canonical partition function for one-dimensional fermionic systems, specifically applying it to derive exact coefficients for the Hubbard model up to order beta^3.

Contribution

It introduces a general relation for the expansion terms of the partition function in 1D fermionic models and applies it to obtain explicit coefficients for the Hubbard model.

Findings

Derived exact coefficients up to order beta^3 for the Hubbard model.

Established a relation linking expansion terms to matrix co-factors.

Validated the approach for any parameter set in the model.

Abstract

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order \beta^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.