Variational Neural-Network Ansatz for Continuum Quantum Field Theory

TL;DR

This paper introduces neural-network quantum field states, a deep learning approach that enables variational studies of non-relativistic quantum field theories in the continuum, overcoming traditional parameterization challenges.

Contribution

The authors develop a neural network ansatz using Deep Sets architecture to parameterize all particle wave functions in quantum field states, facilitating variational analysis.

Findings

Successfully approximated ground states of various field theories.

Demonstrated effectiveness on inhomogeneous and long-range interaction systems.

Provided a new computational tool for quantum field theory research.

Abstract

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In non-relativistic quantum field theories, the challenge is to parameterize and optimize over the infinitely many $n$-particle wave functions comprising the state's Fock space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to non-relativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parameterize all of the $n$-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.