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Quantum Loop Topography for Machine Learning

Yi Zhang and Eun-Ah Kim
Phys. Rev. Lett. 118, 216401 – Published 22 May 2017
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Abstract

Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems, training neural networks to identify quantum phases is a nontrivial challenge. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of nonlocal properties. Here, we introduce quantum loop topography (QLT): a procedure of constructing a multidimensional image from the “sample” Hamiltonian or wave function by evaluating two-point operators that form loops at independent Monte Carlo steps. The loop configuration is guided by the characteristic response for defining the phase, which is Hall conductivity for the cases at hand. Feeding QLT to a fully connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish the Chern insulator and the fractional Chern insulator from trivial insulators with high fidelity. In addition to establishing the first case of obtaining a phase diagram with a topological quantum phase transition with machine learning, the perspective of bridging traditional condensed matter theory with machine learning will be broadly valuable.

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  • Received 15 November 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.216401

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNetworks

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Neural Networks Identify Topological Phases

Published 22 May 2017

A new machine-learning algorithm based on a neural network can tell a topological phase of matter from a conventional one.

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Authors & Affiliations

Yi Zhang* and Eun-Ah Kim

  • Department of Physics, Cornell University, Ithaca, New York 14853, USA and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

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

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Issue

Vol. 118, Iss. 21 — 26 May 2017

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