# Calculating ground state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

## TL;DR

This paper presents a stable and efficient method to incorporate BCS trial wave functions into path-integral quantum Monte Carlo calculations, enhancing the study of strongly correlated fermionic systems with pairing correlations.

## Contribution

It introduces a novel technique for using BCS wave functions in AFQMC, improving efficiency and accuracy, especially in systems with pairing and sign problems.

## Key findings

- Enhanced Monte Carlo sampling efficiency
- Reduced imaginary time for projection in AFQMC
- Successful benchmark results on the attractive Hubbard model

## Abstract

We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection, and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin-balanced (no sign problem) and with a finite spin polarization (with sign problem).