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

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