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arXiv · 2212.00782

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

John M. Martyn·Khadijeh Najafi·Di Luo
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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.

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John M. Martyn, Khadijeh Najafi, Di Luo. 2022-12-01. Variational Neural-Network Ansatz for Continuum Quantum Field Theory. https://doi.org/10.1103/physrevlett.131.081601

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