TY - JOUR

T1 - Quantum Loop Topography for Machine Learning

AU - Zhang, Yi

AU - Kim, Eun Ah

N1 - Funding Information:
This work was supported by the DOE under Award No. DE-SC0010313. Y.Z. acknowledges support through the Bethe Postdoctoral Fellowship and E-AK acknowledges Simons Fellow in Theoretical Physics Award #392182. The bulk of this work was done at KITP supported by Grant No. NSF PHY11-25915.
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/5/22

Y1 - 2017/5/22

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85019848538&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.118.216401

DO - 10.1103/PhysRevLett.118.216401

M3 - Article

C2 - 28598670

AN - SCOPUS:85019848538

SN - 0031-9007

VL - 118

JO - Physical Review Letters

JF - Physical Review Letters

IS - 21

M1 - 216401

ER -