Principal component analysis for fermionic critical points

Natanael C. Costa, Wenjian Hu, Z. J. Bai, Richard T. Scalettar, and Rajiv R. P. Singh
Phys. Rev. B 96, 195138 – Published 20 November 2017

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 Tc. 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.

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  • Received 22 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.195138

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Natanael C. Costa1,2,*, Wenjian Hu2,3, Z. J. Bai3, Richard T. Scalettar2, and Rajiv R. P. Singh2

  • 1Instituto de Fisica, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro RJ, Brazil
  • 2Department of Physics, University of California Davis, California 95616, USA
  • 3Department of Computer Science, University of California Davis, California 95616, USA

  • *natanael@if.ufrj.br

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Vol. 96, Iss. 19 — 15 November 2017

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