Expressivity of determinantal ansatzes for neural network wave functions

Abstract

Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In many cases, the wave function is projected onto a fixed-spin state. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, the full determinant wave function, and a generalized spinor wave function. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed-spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H${}_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds.

References in corpus (5)

• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
• Ground state phases of the two-dimension electron gas with a unified variational approach
• A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions
• An improved penalty-based excited-state variational Monte Carlo approach with deep-learning ansatzes