Nonstochastic algorithms for Jastrow-Slater and correlator product state wave functions

Abstract

Jastrow-Slater and correlator product state wave functions, two classes of quantum many-body wave functions, are commonly studied using Monte Carlo methods with the associated drawbacks of stochastic error. Here we show that efficient nonstochastic algorithms for these wave functions exist, both for observable evaluation and for optimization. The algorithms rely on the structure of these states as a product of local, commuting, invertible operators acting on a simple reference wave function. We describe the nonstochastic energy evaluation and optimization algorithms, and demonstrate them with applications to the Heisenberg and spinless and full Hubbard models. Our results demonstrate that the nonstochastic algorithms yield optimized wave functions and energies very close to those obtained with the variational Monte Carlo algorithm. Such algorithms provide new criteria for identifying new classes of wave functions for efficient computational simulation.

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