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Journal de physique

Pair wave functions for strongly correlated fermions and their determinantal representation

Jean‐Philippe Bouchaud, Antoine Georges, C. Lhuillier

Published Jan 1, 1988• 71 citations
Publisher

Abstract

We show that a (Jastrow projected or not) BCS wave function with any fixed number of fermions can be represented as a determinant. This is important for their numerical investigation, with applications to liquid He3 and Hubbard's model. We also propose a new type of wave function, describing a mixed state composed of paired and unpaired fermions. The physical properties of such a state are tentatively discussed.

DOI
10.1051/jphys:01988004904055300

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We show that a (Jastrow projected or not) BCS wave function with any fixed number of fermions can be represented as a determinant. This is important for their numerical investigation, with applications to liquid He3 and Hubbard's model. We also propose a new type of wave function, describing a mixed state composed of paired and unpaired fermions. The physical properties of such a state are tentatively discussed.
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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).