Machine learning quantum phases of matter beyond the fermion sign problem

2016/08/28 by Peter Broecker, Juan Carrasquilla, Roger G. Melko +1 · 10 citations
Materials Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Computer science #Convolutional neural network #Fermion #Field (mathematics) #Function (biology) #Machine Learning in Materials Science #Mathematics #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Sign (mathematics) #Statistical mechanics #Statistical physics #Statistics #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1038/s41598-017-09098-0

published as Scientific Reports 7, 8823 (2017) · Comments: 8 pages, 6 figures

arxiv created 2016/08/28 · openalex publication_date 2017/08/14 · arxiv updated 2017/08/23 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06

Abstract

State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green's function holds sufficient information to allow for the distinction of different fermionic phases via a CNN. We demonstrate that this QMC + machine learning approach works even for systems exhibiting a severe fermion sign problem where conventional approaches to extract information from the Green's function, e.g. in the form of equal-time correlation functions, fail.

Citations

• Adam: A Method for Stochastic Optimization
• Deep learning and the renormalization group
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• Fermi-liquid instabilities at magnetic quantum phase transitions
• Deep Learning in Neural Networks: An Overview
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