Determinant-free fermionic wave function using feed-forward neural networks
This work addresses a computational bottleneck in quantum many-body physics for researchers, offering incremental improvements to variational Monte Carlo methods.
The authors tackled the computational bottleneck of Slater determinants in fermionic many-body ground state calculations by proposing a determinant-free framework using feed-forward neural networks, reducing the cost from O(N^3) to O(N^2) or less and demonstrating efficiency on a two-dimensional Hubbard model.
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.