Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

Abstract

We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from $r_s=1$ to $r_s=100$, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ansätze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high quality wave functions in computing the reduced single particle density matrix. This contribution establishes neural network models as flexible and high precision Ansätze for periodic electronic systems, an important step towards applications to crystalline solids.

References in corpus (7)

• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• Energies of the first row atoms from quantum Monte Carlo
• Ab initio calculation of real solids via neural network ansatz
• Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
• Towards efficient and accurate \emph{ab initio} solutions to periodic systems via transcorrelation and coupled cluster theory
• Orbital-dependent backflow wave functions for real-space quantum Monte Carlo
• Neural-Network Quantum States for Periodic Systems in Continuous Space

Cited by in corpus (31)

• Ab-initio quantum chemistry with neural-network wavefunctions
• First principles simulations of dense hydrogen
• Ab initio calculation of real solids via neural network ansatz
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas
• DeepQMC: an open-source software suite for variational optimization of deep-learning molecular wave functions
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation
• Deep Variational Free Energy Approach to Dense Hydrogen
• Ground state phases of the two-dimension electron gas with a unified variational approach
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
• Is attention all you need to solve the correlated electron problem?
• Neural Wave Functions for Superfluids
• Taming Landau level mixing in fractional quantum Hall states with deep learning
• Training models using forces computed by stochastic electronic structure methods
• Nematic metal in a multi-valley electron gas: Variational Monte Carlo analysis and application to AlAs
• Electric Polarization from Many-Body Neural Network Ansatz
• Second-order optimisation strategies for neural network quantum states
• A deep neural network approach to solve the Dirac equation
• Deep learning quantum Monte Carlo for solids
• Neutral band gap of carbon by quantum Monte Carlo methods
• Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states
• Shifting sands of hardware and software in exascale quantum mechanical simulations
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters
• Determinant- and Derivative-Free Quantum Monte Carlo Within the Stochastic Representation of Wavefunctions
• Orbital Mixer: Using Atomic Orbital Features for Basis Dependent Prediction of Molecular Wavefunctions
• Neural Wave Functions for High-Pressure Atomic Hydrogen
• Correlation energy of the spin-polarized electron liquid by quantum Monte Carlo
• Convergence of variational Monte Carlo simulation and scale-invariant pre-training
• Expressivity of determinantal ansatzes for neural network wave functions