Machine Learning Phases of Strongly Correlated Fermions

Abstract

Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural-network machine learning techniques to distinguish finite-temperature phases of the strongly correlated fermions on cubic lattices. We show that a three dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling. This transfer learning approach predicts that the instability to the magnetic phase extends to at least 5% doping in this region. Our results pave the way for other machine learning applications in correlated quantum many-body systems.

9 pages, 8 figures

References in corpus (7)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Big Data of Materials Science - Critical Role of the Descriptor
• Discovering Phase Transitions with Unsupervised Learning
• Learning Thermodynamics with Boltzmann Machines
• Machine learning for many-body physics: The case of the Anderson impurity model
• Geometry Dependence of the Sign Problem

Cited by in corpus (191)

• Transfer learning in hybrid classical-quantum neural networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• The Expressive Power of Parameterized Quantum Circuits
• Machine Learning Topological States
• Machine Learning Topological Invariants with Neural Networks
• Approximating quantum many-body wave-functions using artificial neural networks
• Unsupervised machine learning and band topology
• 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
• Quantum Adversarial Machine Learning
• Kernel methods for interpretable machine learning of order parameters
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Identifying Quantum Phase Transitions with Adversarial Neural Networks
• Machine Learning ${\mathbb{Z}}_2$ Quantum Spin Liquids with Quasi-particle Statistics
• Machine learning of phase transitions in the percolation and XY models
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Neural Network-based Classification of Crystal Symmetries from X-Ray Diffraction Patterns
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Regressive and generative neural networks for scalar field theory
• Discriminative Cooperative Networks for Detecting Phase Transitions
• Solving frustrated quantum many-particle models with convolutional neural networks
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Machine learning of quantum phase transitions
• Topological quantum phase transitions retrieved through unsupervised machine learning
• Topological Quantum Compiling with Reinforcement Learning
• Unveiling phase transitions with machine learning
• Deep Learning and AdS/CFT
• Machine Learning for Condensed Matter Physics
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Unsupervised machine learning of topological phase transitions from experimental data
• Deep Learning Topological Invariants of Band Insulators
• Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization
• Probing hidden spin order with interpretable machine learning
• Analytic continuation via domain-knowledge free machine learning
• Unifying Neural-network Quantum States and Correlator Product States via Tensor Networks
• Learning Disordered Topological Phases by Statistical Recovery of Symmetry
• Machine Learning Bell Nonlocality in Quantum Many-body Systems
• Machine learning non-local correlations
• Machine Learning Topological Phases with a Solid-state Quantum Simulator
• A comparative study of feature selection methods for stress hotspot classification in materials
• Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase
• Machine learning action parameters in lattice quantum chromodynamics
• Real space mapping of topological invariants using artificial neural networks
• Super-resolving the Ising model with convolutional neural networks
• Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
• Learning multiple order parameters with interpretable machines
• Machine Learning meets Quantum Foundations: A Brief Survey
• Learning entropy production via neural networks
• Learning phase transitions from dynamics
• Smallest Neural Network to Learn the Ising Criticality
• Unsupervised machine learning of quantum phase transitions using diffusion maps
• Supervised learning magnetic skyrmion phases
• Nuclear liquid-gas phase transition with machine learning
• Markovian Quantum Neuroevolution for Machine Learning
• Machine Learning as a universal tool for quantitative investigations of phase transition
• Automated discovery of characteristic features of phase transitions in many-body localization
• Principal Component Analysis for Fermionic Critical Points
• Matrix Product Operators for Sequence to Sequence Learning
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Machine learning density functional theory for the Hubbard model
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Machine learning topological phases in real space
• Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
• Interpreting machine learning of topological quantum phase transitions
• Machine learning \& artificial intelligence in the quantum domain
• Mapping distinct phase transitions to a neural network
• Predicting quantum advantage by quantum walk with convolutional neural networks
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Machine learning for molecular dynamics with strongly correlated electrons
• Neural-network-designed pulse sequences for robust control of singlet-triplet qubits
• A machine-learning solver for modified diffusion equations
• Interpretable machine learning for inferring the phase boundaries in a nonequilibrium system
• Visualizing Strange Metallic Correlations in the 2D Fermi-Hubbard Model with AI
• Accelerating lattice quantum Monte Carlo simulation using artificial neural networks: an application to the Holstein model
• Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
• Topological Persistence Machine of Phase Transitions
• Machine Learning of Implicit Combinatorial Rules in Mechanical Metamaterials
• Machine Learning Prediction of DNA Charge Transport
• Extending machine learning classification capabilities with histogram reweighting
• Unsupervised learning using topological data augmentation
• Construction of Hamiltonians by supervised learning of energy and entanglement spectra
• Revealing quantum chaos with machine learning
• Investigating Topological Order using Recurrent Neural Networks
• Extracting Critical Exponent by Finite-Size Scaling with Convolutional Neural Networks
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Quantum kernels to learn the phases of quantum matter
• Interpretable and unsupervised phase classification
• Few-shot machine learning in the three-dimensional Ising model
• Self-organizing maps as a method for detecting phase transitions and phase identification
• Approximating power of machine-learning ansatz for quantum many-body states
• Deep neural networks for direct, featureless learning through observation: the case of 2d spin models
• Accelerated variational algorithms for digital quantum simulation of many-body ground states
• Artificial Neural Network Based Computation for Out-of-Time-Ordered Correlators
• Machine-learning-corrected quantum dynamics calculations
• Machine learning electron correlation in a disordered medium
• Identifying Product Order with Restricted Boltzmann Machines
• A Neural Networks study of the phase transitions of Potts model
• Visualizing Quantum Phases And Identifying Quantum Phase Transitions By Nonlinear Dimensionality Reduction
• Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks
• Learning quantum phase transitions through Topological Data Analysis
• Designing quantum many-body matter with conditional generative adversarial networks
• Deep Learning-Assisted Classification of Site-Resolved Quantum Gas Microscope Images
• Machine learning effective models for quantum systems
• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Transforming Generalized Ising Model into Boltzmann Machine
• Detected the steerability bounds of the generalized Werner states via BackPropagation neural network
• Transfer learning of phase transitions in percolation and directed percolation
• Distinguishing an Anderson Insulator from a Many-Body Localized phase through space-time snapshots with Neural Networks
• A learning by confusion approach to characterize phase transitions
• Reducing the Quantum Many-electron Problem to Two Electrons with Machine Learning
• Extracting many-particle entanglement entropy from observables using supervised machine learning
• Random matrix analysis of deep neural network weight matrices
• Classifying surface probe images in strongly correlated electronic systems via machine learning
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Machine learning phases and criticalities without using real data for training
• Visualizing Neural Network Developing Perturbation Theory
• Optical lattice experiments at unobserved conditions and scales through generative adversarial deep learning
• Multi-faceted machine learning of competing orders in disordered interacting systems
• Learning Order Parameters from Videos of Dynamical Phases for Skyrmions with Neural Networks
• Machine learning of XY model on a spherical Fibonacci lattice
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods
• Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems
• Supervised and Unsupervised Machine Learning of Structural Phases of Polymers Adsorbed to Nanowires
• The percolating cluster is invisible to image recognition with deep learning
• Learning entanglement breakdown as a phase transition by confusion
• Topological defects and confinement with machine learning: the case of monopoles in compact electrodynamics
• Magnetic Phases of Spatially-Modulated Spin-1 Chains in Rydberg Excitons: Classical and Quantum Simulations
• Machine learning for structure-property relationships: Scalability and limitations
• Quantum entanglement recognition
• Learning the Fuzzy Phases of Small Photonic Condensates
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter
• Probing Criticality in Quantum Spin Chains with Neural Networks
• Random Sampling Neural Network for Quantum Many-Body Problems
• Machine learning phases of active matter
• Adversarial Machine Learning Phases of Matter
• Learning to find order in disorder
• Casimir effect with machine learning
• Phase determination with and without deep learning
• Variational Autoencoder Analysis of Ising Model Statistical Distributions and Phase Transitions
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• A simple framework for contrastive learning phases of matter
• Watch and learn -- a generalized approach for transferrable learning in deep neural networks via physical principles
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Robust Identification of Topological Phase Transition by Self-Supervised Machine Learning Approach
• Atom Cloud Detection Using a Deep Neural Network
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Predicting quantum many-body dynamics with transferable neural networks
• Supervised and unsupervised learning of the many-body critical phase, phase transitions, and critical exponents in disordered quantum systems
• Observation of non-Fermi liquid physics in a quantum critical metal via quantum loop topography
• Experimentally detecting a quantum change point via Bayesian inference
• Dual-Capability Machine Learning Models for Quantum Hamiltonian Parameter Estimation and Dynamics Prediction
• Ground-state properties via machine learning quantum constraints
• Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning
• Probing transport in quantum many-fermion simulations via quantum loop topography
• A sampling-guided unsupervised learning method to capture percolation in complex networks
• Hamming Distance and the onset of quantum criticality
• Extracting Off-Diagonal Order from Diagonal Basis Measurements
• Entanglement transitions from restricted Boltzmann machines
• Learning What a Machine Learns in a Many-Body Localization Transition
• Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning
• Boundary between noise and information applied to filtering neural network weight matrices
• Application of Machine Learning to Sporadic Experimental Data for Understanding Epitaxial Strain Relaxation
• Deep Learning the Forecast of Galactic Cosmic-Ray Spectra
• Probing topological properties of 3D lattice dimer model with neural networks
• Fluctuation based interpretable analysis scheme for quantum many-body snapshots
• Phase classification in the long-range Harper model using machine learning
• Renormalization-group-inspired neural networks for computing topological invariants
• Learning phases with Quantum Monte Carlo simulation cell
• A new strategy for directly calculating the minimum eigenvector of matrices without diagonalization
• Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems
• Establishing simple relationship between eigenvector and matrix elements
• Weighted Quantum Channel Compiling through Proximal Policy Optimization
• Many-body mobility edges in 1D and 2D revealed by convolutional neural networks
• Deep Learning Super-Diffusion in Multiplex Networks
• Confusion-driven machine learning of structural phases of a flexible, magnetic Stockmayer polymer
• A Group-Equivariant Autoencoder for Identifying Spontaneously Broken Symmetries
• Entanglement Clustering for ground-stateable quantum many-body states
• Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime
• Efficiency of neural-network state representations of one-dimensional quantum spin systems
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty
• Machine learning of the Ising model on a spherical Fibonacci lattice
• Machine learning in physics: The pitfalls of poisoned training sets
• Optimized Observable Readout from Single-shot Images of Ultracold Atoms via Machine Learning
• Learning a compass spin model with neural network quantum states
• A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography
• Autonomous Discovery of the Ising Model's Critical Parameters with Reinforcement Learning