Principal Component Analysis for Fermionic Critical Points

TL;DR

This paper combines determinant Quantum Monte Carlo with PCA to identify phase transitions in various strongly correlated electron models, offering a new unsupervised learning approach to analyze critical phenomena.

Contribution

It introduces a novel application of PCA to DQMC data for detecting phase transitions across multiple models, including finite temperature superconductivity and charge density waves.

Findings

Successfully identified phase transitions in several models.

Demonstrated PCA's effectiveness on different auxiliary field configurations.

Provided finite size scaling analysis for critical temperature determination.

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.