Perturbation Expansion of the Partition Sum for any Temperature

TL;DR

This paper introduces a perturbation theory for the partition sum applicable at any temperature, including degenerate Hamiltonians, demonstrated through the Hubbard model.

Contribution

It presents a novel perturbation approach based on Liouville eigenoperators that works universally across temperatures and handles degeneracies.

Findings

Second order correction matches known results

Method is reliable for various temperature regimes

Applicable to models with degenerate Hamiltonians

Abstract

Based on the special properties of Liouville eigenoperators a perturbation theory for the partition sum is given. It is applicable for any temperature and includes the case of degenerate Hamiltonians. To demonstrate the reliability of the method, the second order correction to the atomic limit grand canonical potential of the Hubbard model is calculated and compared to results known from the literature.