Principal Component Analysis for Fermionic Critical Points

Abstract

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

arXiv comment11 pages, 8 figures

References in corpus (36)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• Interactions and phase transitions on graphene's honeycomb lattice
• Quantum Entanglement in Neural Network States
• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Machine learning quantum phases of matter beyond the fermion sign problem
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice
• Quantum Loop Topography for Machine Learning
• Machine Learning Phases of Strongly Correlated Fermions
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Probing many-body localization with neural networks
• Unsupervised Learning of Frustrated Classical Spin Models I: Principle Component Analysis
• Quantum Monte Carlo simulations of the half-filled two-dimensional Kondo lattice model
• Ferromagnetism in Hubbard Models
• Critical temperature for the two-dimensional attractive Hubbard Model
• Competition Between Antiferromagnetic Order and Spin-Liquid Behavior in the Two-Dimensional Periodic Anderson Model at Half-Filling
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-Learning Determinantal Quantum Monte Carlo Method
• Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Quantum phase recognition via unsupervised machine learning
• Magnetic and Thermodynamic Properties of the Three-Dimensional Periodic Anderson Hamiltonian
• Ferromagnetism beyond Lieb's theorem
• Recommender Engine for Continuous Time Quantum Monte Carlo Methods
• Pairing, Charge, and Spin Correlations in the Three-Band Hubbard Model
• Effects of an Additional Conduction Band on Singlet-Antiferromagnet Competition in the Periodic Anderson Model
• Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach
• Doping-dependent study of the periodic Anderson model in three dimensions

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• Topological quantum phase transitions retrieved through unsupervised machine learning
• Deep Learning and AdS/CFT
• Deep Learning Topological Invariants of Band Insulators
• Charge Order in the Holstein Model on a Honeycomb Lattice
• Phonon dispersion and the competition between pairing and charge order
• Measurement-induced criticality as a data-structure transition
• Smallest Neural Network to Learn the Ising Criticality
• Superconductivity and charge density wave order in the 2D Holstein model
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Machine Learning of Frustrated Classical Spin Models. II. Kernel Principal Component Analysis
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Mapping distinct phase transitions to a neural network
• Extending machine learning classification capabilities with histogram reweighting
• Unsupervised learning using topological data augmentation
• Intrinsic dimension of path integrals: data mining quantum criticality and emergent simplicity
• A perspective on machine learning and data science for strongly correlated electron problems
• Principal Component Analysis of collective flow in Relativistic Heavy-Ion Collisions
• Self-organizing maps as a method for detecting phase transitions and phase identification
• Visualizing Quantum Phases And Identifying Quantum Phase Transitions By Nonlinear Dimensionality Reduction
• Learning quantum phase transitions through Topological Data Analysis
• Unsupervised machine learning approaches to the $q$-state Potts model
• Quantum Monte Carlo study of an anharmonic Holstein model
• Visualizing Neural Network Developing Perturbation Theory
• Data-driven discovery of statistically relevant information in quantum simulators
• Supervised and Unsupervised Machine Learning of Structural Phases of Polymers Adsorbed to Nanowires
• Complexity of spin configurations dynamics due to unitary evolution and periodic projective measurements
• Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
• Supersolid Phase in the Diluted Holstein Model
• Confusion-driven machine learning of structural phases of a flexible, magnetic Stockmayer polymer
• Optimized Observable Readout from Single-shot Images of Ultracold Atoms via Machine Learning
• Spin-resolved Mott crossover and entanglement in the half-filled Hubbard model