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 (23)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Ab-initio quantum chemistry with neural-network wavefunctions
• Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• Ab initio calculation of real solids via neural network ansatz
• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States
• Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas
• Spin-Orbit Interactions in Electronic Structure Quantum Monte Carlo
• Quantum Monte Carlo study of the two-dimensional electron gas in presence of Rashba interaction
• DeepQMC: an open-source software suite for variational optimization of deep-learning molecular wave functions
• Quantum Monte Carlo with Variable Spins
• Deep Variational Free Energy Approach to Dense Hydrogen
• 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