Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order $\beta^5$

TL;DR

This paper derives exact analytical coefficients for the grand-canonical partition function of the 1D Hubbard model up to order β^5 using Grassmann algebra, providing non-perturbative results applicable at high temperatures.

Contribution

It introduces an alternative Grassmann algebra-based method to compute the partition function coefficients of the 1D Hubbard model up to fifth order in β, without parameter restrictions.

Findings

Analytical coefficients for the partition function up to β^5.

Non-perturbative thermodynamic results at high temperature.

Applicability to arbitrary electron density.

Abstract

We calculate the exact analytical coefficients of the $\beta$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order $\beta^5$, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.