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Title: Machine learning $$\mathbb{Z}_2$$ quantum spin liquids with quasiparticle statistics

Journal Article · · Physical Review. B
 [1];  [2];  [1]
  1. Cornell University, Ithaca, NY (United States)
  2. Perimeter Institute for Theoretical Physics, Waterloo (Canada); University of Waterloo, ON (Canada)
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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. In this report 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 $$\mathbb{Z}_2$$ 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.

Research Organization:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC); Bethe Postdoctoral Fellowship; Simons Fellow in Theoretical Physics Award; Natural Sciences and Engineering Research Council of Canada (NSERC); Industry Canada; Ministry of Research & Innovation.
Grant/Contract Number:
SC0010313; 392182; de-sc0010313
OSTI ID:
1540749
Alternate ID(s):
OSTI ID: 1413081
Journal Information:
Physical Review. B, Vol. 96, Issue 24; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 81 works
Citation information provided by
Web of Science

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Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
machine learning
quantum spin liquid
topological phase transition
topological phase of matter