Accelerating lattice quantum Monte Carlo simulation using artificial neural networks: an application to the Holstein model

Abstract

Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input features and can, therefore, be trained using samples generated by conventional MC runs on smaller lattices before being utilized for simulations on larger systems. This new approach is benchmarked for the case of determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein model. We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order of magnitude speedup over the conventional DQMC algorithm. Our approach is broadly applicable to many classical and quantum lattice MC algorithms.

6 pages, 3 figures

References in corpus (29)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Machine Learning Topological States
• Quantum Loop Topography for Machine Learning
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Self-Learning Monte Carlo Method
• Generative Adversarial Networks recover features in astrophysical images of galaxies beyond the deconvolution limit
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Machine Learning in Electronic Quantum Matter Imaging Experiments
• Neural Network Renormalization Group
• Probing many-body localization with neural networks
• Neural Networks for Modeling and Control of Particle Accelerators
• Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-Learning Determinantal Quantum Monte Carlo Method
• Self-learning Monte Carlo with Deep Neural Networks
• Self-Learning Monte Carlo Method: Continuous-Time Algorithm
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Machine learning density functional theory for the Hubbard model
• Machine learning for molecular dynamics with strongly correlated electrons
• Projective quantum Monte Carlo simulations guided by unrestricted neural network states
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Parallelized Traveling Cluster Approximation to Study Numerically Spin-Fermion Models on Large Lattices

Cited by in corpus (23)

• Machine Learning for Quantum Matter
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Adaptive 3D convolutional neural network-based reconstruction method for 3D coherent diffraction imaging
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Extending machine learning classification capabilities with histogram reweighting
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• A perspective on machine learning and data science for strongly correlated electron problems
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions (version 2.0 release)
• Charge Density Wave and Superconductivity in the Disordered Holstein Model
• Machine learning for phase ordering dynamics of charge density waves
• The two-dimensional $t$-$t^{\prime }$ Holstein model
• Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models
• Polaron and bipolaron tendencies in a semiclassical model for hole-doped bismuthates
• Variational Autoencoder Analysis of Ising Model Statistical Distributions and Phase Transitions
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Reducing autocorrelation time in determinant quantum Monte Carlo using Wang-Landau algorithm: application to Holstein model
• Charge correlations suppress unconventional pairing in the Holstein model
• A Group-Equivariant Autoencoder for Identifying Spontaneously Broken Symmetries
• Discovering quasiorder parameters in the Potts model: A bridge between machine learning and critical phenomena
• Adaptive Latent Space Tuning for Non-Stationary Distributions