Analysis of Kohn-Sham Eigenfunctions Using a Convolutional Neural Network in Simulations of the Metal-insulator Transition in Doped Semiconductors

Abstract

Machine learning has recently been applied to many problems in condensed matter physics. A common point of many proposals is to save computational cost by training the machine with data from a simple example and then using the machine to make predictions for a more complicated example. Convolutional neural networks (CNN), which are one of the tools of machine learning, have proved to work well for assessing eigenfunctions in disordered systems. Here we apply a CNN to assess Kohn-Sham eigenfunctions obtained in density functional theory (DFT) simulations of the metal-insulator transition of a doped semiconductor. We demonstrate that a CNN that has been trained using eigenfunctions from a simulation of a doped semiconductor that neglects electron spin successfully predicts the critical concentration when presented with eigenfunctions from simulations that include spin.

7pages, 7 figures

References in corpus (14)

• The Kernel Polynomial Method
• Learning phase transitions by confusion
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Conceptual and practical bases for the high accuracy of machine learning interatomic potential
• Bayesian optimization of chemical composition: a comprehensive framework and its application to $R$Fe${}_{12}$-type magnet compounds
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Data Assimilation Method for Experimental and First-Principles Data: Finite-Temperature Magnetization of (Nd,Pr,La,Ce)${}_2$(Fe,Co,Ni)${}_{14}$B
• Quantum percolation transition in 3d: density of states, finite size scaling and multifractality
• Multifractality of ab initio wave functions in doped semiconductors