Approximating Grassmann valued path integrals with radial basis function neural networks

Abstract

Solving path integrals in quantum field theories often involves the numerical handling of noncommuting Grassmann fields, which is in many cases a highly nontrivial and numerically inefficient task, especially in large systems and at higher dimensions. In this paper a radial basis function type neural network construction is used to approximate fermionic path integrals that include local couplings in their hopping terms. By isolating the interaction terms from the purely fermionic components using a radial basis function expansion, the path integral can be approximated by a few percent accuracy even for very large lattice sizes. The method has been developed and tested using staggered fermions in one, and in two dimensions, through calculating the partition functions, and expectation values.

References in corpus (18)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• The QCD equation of state at nonzero densities: lattice result
• Finite-density lattice QCD and sign problem: current status and open problems
• Solving the Bose-Hubbard model with machine learning
• Meson Screening Masses in (2+1)-Flavor QCD
• A lattice theory for low energy fermions at finite chemical potential
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• Lattice Monte Carlo calculations for unitary fermions in a harmonic trap
• A local factorization of the fermion determinant in lattice QCD
• Wilson Fermion Determinant in Lattice QCD
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Fixed-energy inverse scattering with radial basis function neural networks and its application to neutron-alpha interactions
• Conformal Fields from Neural Networks
• Efficient Solutions of Fermionic Systems using Artificial Neural Networks
• Machine-learned RG-improved gauge actions and classically perfect gradient flows
• Addressing the sign-problem in Euclidean path integrals with radial basis function neural networks
• Neural network expansion of Euclidean path integrals and its application to interacting scalar fields