Toward an automated-algebra framework for high orders in the virial expansion of quantum matter

TL;DR

This paper reviews automated algebra methods for calculating high-order virial coefficients in quantum many-body systems, enabling non-stochastic, analytic, and parallelizable computations of thermodynamic properties.

Contribution

It introduces a comprehensive, non-stochastic algebraic framework for efficiently computing high-order virial coefficients in quantum matter.

Findings

Calculated virial coefficients for thermodynamic quantities

Demonstrated methods' applicability to trapped and homogeneous systems

Outlined generalizations to other observables like Tan's contact

Abstract

The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing (if not solving) the quantum $n$-body problem. In this work, we present a comprehensive review of automated algebra methods, which we developed to calculate high-order virial coefficients. The methods are computational but non-stochastic, thus avoiding statistical effects; they are also for the most part analytic, not numerical, and amenable to massively parallel computer architectures. We show formalism and results for coefficients characterizing the thermodynamics (pressure, density, energy, static susceptibilities) of homogeneous and harmonically trapped systems, and explain how to generalize them to other observables such as the momentum distribution, Tan's contact, and the structure factor.