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Speaker: Zhi-Yu Xiao from the College of William and Mary
Title: A Pseudo-BCS Wavefunction from Density Matrix Decomposition: Application in Auxiliary-Field Quantum Monte Carlo.
Abstract: In this talk, I will 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). I will 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. I will 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 and some molecules as examples. The preprint for most part of this work can be found at https://arxiv.org/abs/2010.06055 .