Grassmann Algebra and Fermions at Finite Temperature

TL;DR

This paper introduces a novel Grassmann algebra-based method for calculating high-temperature expansion coefficients of fermionic models' partition functions, demonstrated on the Hatsugai-Kohmoto model.

Contribution

It presents a new approach leveraging Grassmann integrals for fermionic models, simplifying calculations of high-temperature expansions.

Findings

Successfully applied to the Hatsugai-Kohmoto model

Reproduced known results with the new method

Provides a systematic way to handle fermionic operators at finite temperature

Abstract

For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai-Kohmoto model, reobtaining well-known results.