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.

References in corpus (32)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Learning phase transitions by confusion
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Self-Learning Monte Carlo Method
• Efficient DMFT-simulation of the Holstein-Hubbard Model
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Machine learning vortices at the Kosterlitz-Thouless transition
• Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory
• Anomalously Strong Near-Neighbor Attraction in Doped 1D Cuprate Chains
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Metallicity in the half-filled Holstein-Hubbard model
• Bipolaronic high-temperature superconductivity
• Spin Density Waves in the Hubbard model - A DMFT approach
• Charge order and antiferromagnetism in the extended Hubbard model
• Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
• Classical spin dynamics based on SU($N$) coherent states
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Geometric integration of classical spin dynamics via a mean-field Schrödinger equation
• Particle-hole asymmetry in the dynamical spin and charge structure factors of the corner-shared one-dimensional cuprates
• Stripe correlations in the two-dimensional Hubbard-Holstein model
• Interplay of Site and Bond Electron-Phonon Coupling in One Dimension
• Marshall-positive SU($N$) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians
• Interplay of charge, spin and lattice degrees of freedom on the spectral properties of the one-dimensional Hubbard-Holstein model
• Bond excitations in the pseudogap phase of the Hubbard Model

Cited by in corpus (8)

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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
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning