A perspective on machine learning and data science for strongly correlated electron problems

Abstract

Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times, challenges in recognizing novel phases, and the Fermion sign problem. Methods in machine learning (ML), artificial intelligence, and data science promise to help address these limitations and open up a new frontier in strongly correlated quantum system simulations. In this paper, we review some of the progress in this area. We begin by examining these approaches in the context of classical models, where their underpinnings and application can be easily illustrated and benchmarked. We then discuss cases where ML methods have enabled scientific discovery. Finally, we will examine their applications in accelerating model solutions in state-of-the-art quantum many-body methods like quantum Monte Carlo and discuss potential future research directions.

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• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Extracting Off-Diagonal Order from Diagonal Basis Measurements
• Fluctuation based interpretable analysis scheme for quantum many-body snapshots
• Learning phases with Quantum Monte Carlo simulation cell
• A Group-Equivariant Autoencoder for Identifying Spontaneously Broken Symmetries
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning