Expansion for Quantum Statistical Mechanics Based on Wave Function Symmetrization

TL;DR

This paper introduces a new expansion method for quantum statistical mechanics based on wave function symmetrization, providing a more rapidly converging approach with practical applications for simulating condensed matter quantum systems.

Contribution

It derives a quantum statistical mechanics expansion using permutation loops, improving convergence and simplicity over existing methods like the Lee-Yang expansion.

Findings

Full fugacity expansion for the quantum ideal gas

Second fugacity coefficient for interacting quantum particles

Expected faster convergence compared to Lee-Yang virial expansion

Abstract

An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the symmetrization of the wave function with respect to localized particle interchange. Explicit application of the theory yields the full fugacity expansion for the quantum ideal gas, and the second fugacity coefficient for interacting quantum particles, which agree with known results. Compared to the Lee-Yang virial cluster expansion, the present expansion is expected to be more rapidly converging and the individual terms appear to be simpler to evaluate. The results obtained in this paper are intended for practical computer simulation algorithms for terrestrial condensed matter quantum systems.