Pseudo-BCS wave function from density matrix decomposition: Application in auxiliary-field quantum Monte Carlo

Abstract

We present a method to construct pseudo-BCS wave functions from the one-body density matrix. The resulting many-body wave function, which can be produced for any fermion systems, including those with purely repulsive interactions, has the form of a number-projected BCS form, or antisymmetrized geminal power (AGP). Such wave functions provide a better ansatz for correlated fermion systems than a single Slater determinant, and often better than a linear combination of Slater determinants (for example from a truncated active space calculation). We describe a procedure to build such a wave function conveniently from a given reduced density matrix of the system, rather than from a mean-field solution (which gives a Slater determinant for repulsive interactions). The pseudo-BCS wave function thus obtained reproduces the density matrix or minimizes the difference between the input and resulting density matrices. One application of the pseudo-BCS wave function is in auxiliary-field quantum Monte Carlo (AFQMC) calculations as the trial wave function to control the sign/phase problem. AFQMC is often among the most accurate general methods for correlated fermion systems. We show that the pseudo-BCS form further reduces the constraint bias and leads to improved accuracy compared to the usual Slater determinant trial wave functions, using the two-dimensional Hubbard model as an example. Furthermore, the pseudo-BCS trial wave function allows a new systematically improvable self-consistent approach, with pseudo-BCS trial wave function iteratively generated by AFQMC via the one-body density matrix.Received 19 October 2020Revised 4 January 2021Accepted 6 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013065Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)TechniquesApproximation methods for many-body systemsBCS theoryHubbard modelQuantum Monte CarloCondensed Matter, Materials & Applied Physics