Determinant-free fermionic wave function using feed-forward neural networks

TL;DR

This paper introduces a neural network-based framework for efficiently approximating the ground state of many-body fermionic systems, reducing computational complexity and improving accuracy through innovative sign calculation and symmetry exploitation.

Contribution

It presents a novel neural network approach that bypasses the traditional Slater determinant bottleneck, lowering computational cost and enhancing variational accuracy in fermionic ground state calculations.

Findings

Reduced computational cost from O(N^3) to O(N^2) or less.

Improved accuracy by optimizing energy variance alongside energy.

Enhanced stability and accuracy using symmetry and neural network techniques.

Abstract

We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater determinant (or Pfaffian), which is a computational bottleneck because of the numerical cost of $O(N^3)$ for $N$ particles. We bypass this bottleneck by explicitly calculating the sign changes associated with particle exchanges in real space and using fully connected neural networks for optimizing the rest parts of the wave function. This reduces the computational cost to $O(N^2)$ or less. We show that the accuracy of the approximation can be improved by optimizing the "variance" of the energy simultaneously with the energy itself. We also find that a reweighting method in Monte Carlo sampling can stabilize the calculation. These improvements can be applied to other approaches based on variational Monte Carlo methods. Moreover, we show that the accuracy can be further improved by using the symmetry of the system, the representative states, and an additional neural network implementing a generalized Gutzwiller-Jastrow factor. We demonstrate the efficiency of the method by applying it to a two-dimensional Hubbard model.