Machine learning Z2 quantum spin liquids with quasiparticle statistics

Yi Zhang, Roger G. Melko, and Eun-Ah Kim
Phys. Rev. B 96, 245119 – Published 13 December 2017

Abstract

After decades of progress and effort, obtaining a phase diagram for a strongly correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these nonlocal observables at many points in phase space can be prohibitively costly. With growing excitement over topological quantum computation comes the need for an efficient approach for obtaining topological phase diagrams. Here we turn to machine learning using quantum loop topography (QLT), a notion we have recently introduced. Specifically, we propose a construction of QLT that is sensitive to quasiparticle statistics. We then use mutual statistics between the spinons and visons to detect a Z2 quantum spin liquid in a multiparameter phase space. We successfully obtain the quantum phase boundary between the topological and trivial phases using a simple feed-forward neural network. Furthermore, we demonstrate advantages of our approach for the evaluation of phase diagrams relating to speed and storage. Such statistics-based machine learning of topological phases opens new efficient routes to studying topological phase diagrams in strongly correlated systems.

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  • Received 20 May 2017
  • Revised 30 October 2017
  • Corrected 12 February 2018

DOI:https://doi.org/10.1103/PhysRevB.96.245119

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Corrections

12 February 2018

Erratum

Authors & Affiliations

Yi Zhang1,*, Roger G. Melko2,3, and Eun-Ah Kim1,†

  • 1Department of Physics, Cornell University, Ithaca, New York 14853, USA
  • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 3Department of Physics and Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada

  • *frankzhangyi@gmail.com
  • eun-ah.kim@cornell.edu

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Issue

Vol. 96, Iss. 24 — 15 December 2017

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