Topological Matter in the Absence of Translational Invariance

Kobayashi, Koji; Ohtsuki, Tomi; Imura, Ken‐Ichiro

doi:10.1002/9781119407317.ch4

Cited by 1 publication

(2 citation statements)

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“…[306][307][308] The present method captures the TAI and gives a phase diagram quantitatively consistent with that obtained by 18/47 the transfer matrix method. 208,305) It should be emphasized that training along a few finite 1D lines in a 2D parameter space enables us to draw the phase diagram. We also note that the phase boundary between OI and STI is colored red, which indicates that the phase on the phase boundary is a metal phase.…”

Section: D Topological Insulatorsmentioning

confidence: 99%

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Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions

Ohtsuki

Mano

2020

J. Phys. Soc. Jpn.

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Applications of neural networks to condensed matter physics are becoming popular and beginning to be well accepted. Obtaining and representing the ground and excited state wave functions are examples of such applications. Another application is analyzing the wave functions and determining their quantum phases. Here, we review the recent progress of using the multilayer convolutional neural network, so-called deep learning, to determine the quantum phases in random electron systems. After training the neural network by the supervised learning of wave functions in restricted parameter regions in known phases, the neural networks can determine the phases of the wave functions in wide parameter regions in unknown phases; hence, the phase diagrams are obtained. We demonstrate the validity and generality of this method by drawing the phase diagrams of two-and higher dimensional Anderson metal-insulator transitions and quantum percolations as well as disordered topological systems such as three-dimensional topological insulators and Weyl semimetals. Both real-space and Fourier space wave functions are analyzed. The advantages and disadvantages over conventional methods are discussed. * ohtsuki@sophia.ac.jp

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Section: D Topological Insulatorsmentioning

confidence: 99%

“…The arrows indicate the lines along which machine learning for STI, WTI(001), and WTI(111) has been performed. Solid lines are results from the transfer matrix estimate 305).…”

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confidence: 99%