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.

11 pages, 8 figures

References in corpus (17)

• Learning phase transitions by confusion
• Interactions and phase transitions on graphene's honeycomb lattice
• Quantum Entanglement in Neural Network States
• Discovering Phases, Phase Transitions and Crossovers through Unsupervised Machine Learning: A critical examination
• 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
• 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
• Self-Learning Monte Carlo Method in Fermion Systems
• Self-Learning Determinantal Quantum Monte Carlo Method
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Quantum phase recognition via unsupervised machine learning
• Ferromagnetism beyond Lieb's theorem
• Recommender Engine for Continuous Time Quantum Monte Carlo Methods
• Effects of an Additional Conduction Band on Singlet-Antiferromagnet Competition in the Periodic Anderson Model

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