Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems

TL;DR

This paper introduces a wave function approach for calculating thermal averages in many-fermion systems within the canonical ensemble, utilizing projection techniques and correlation methods.

Contribution

It develops a novel wave function representation for the canonical thermal state and explores correlation schemes beyond mean-field approximation.

Findings

Effective wave function representation for canonical thermal states

Benchmark results on Hydrogen molecule and Hubbard model

Comparison of correlation schemes in fermionic systems

Abstract

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. The resulting canonical thermal state obeys an imaginary time-evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state, and by adding correlation to the number-projected mean-field state. As benchmark examples, we use number-projected configuration interaction and an AGP-based perturbation theory to study the Hydrogen molecule in a minimal basis and the six-site Hubbard model.