About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators

TL;DR

This paper presents a general method to resolve sign ambiguities in evaluating grand-canonical traces of quasi-particle density operators, crucial for accurate finite-temperature quantum many-body calculations.

Contribution

It introduces a simple, universal prescription to unambiguously determine the sign of traces involving determinants in quantum statistical calculations.

Findings

The method reliably resolves sign ambiguities in grand-canonical trace evaluations.

Comparison shows the method's effectiveness over the numerical continuity approach.

Application to projected partition functions improves calculation accuracy.

Abstract

A simple and general prescription for evaluating unambiguously the sign of the grand-canonical trace of quasi-particle statistical density operators (the so-called sign ambiguity in taking the square root of determinants) is given. Sign ambiguities of this kind appear in the evaluation of the grand-canonical partition function projected to good quantum numbers (angular momentum, parity and particle number) in the Hartree-Fock-Bogoliubov approximation at finite temperature, since traces are usually expressed as the square root of determinants. A comparison is made with the numerical continuity method.