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arXiv:1609.02552 · Physical Review X

Machine Learning Phases of Strongly Correlated Fermions

Kelvin Ch’ng, Juan Carrasquilla, Roger G. Melko, Ehsan Khatami

Published Aug 30, 2017• 317 citations
arXivHTMLPDF

Abstract

Machine learning has strong potential as a tool for understanding how to classify phases in condensed matter physics. A new investigation shows that an artificial neural network can be trained to identify changes in the collective magnetic properties of electrons on a lattice and predict trends in the transition when some of the electrons are removed.

DOI
10.1103/physrevx.7.031038

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Machine learning has strong potential as a tool for understanding how to classify phases in condensed matter physics. A new investigation shows that an artificial neural network can be trained to identify changes in the collective magnetic properties of electrons on a lattice and predict trends in the transition when some of the electrons are removed.
The identification and characterization of phase transitions is one of the oldest and most central problems in condensed matter physics, traditionally approached through order parameters, free-energy expansions, renormalization-group analysis, and direct numerical simulation. Over the past decade, machine learning (ML) has emerged as a complementary and, in some regimes, transformative methodology for this task. Supervised classifiers can learn to distinguish phases directly from raw configurations without an a priori order parameter; unsupervised and self-supervised techniques such as principal component analysis, autoencoders, and learning-by-confusion can locate transition points with minimal or no labeled data; and generative and variational architectures, including neural-network quantum states, now approximate ground-state wavefunctions of strongly correlated systems well beyond the reach of exact diagonalization. This paper reviews the theoretical foundations of phase transitions relevant to machine-learning applications, surveys the principal families of algorithms used to detect and classify phases, and examines their application across classical spin systems, percolation, topological and quantum phases, strongly correlated electron systems, and experimentally measured spectroscopic data. Representative case studies are discussed, including convolutional and graph-neural-network classifiers of lattice configurations, explainable-ML detection of thermodynamic transitions in photoemission spectra, and deep-learning-guided discovery of high-temperature superconductors. The review closes with a critical discussion of persistent challenges interpretability, data scarcity in correlated-electron experiments, generalization across Hamiltonians, and the reliability of learned order parameters near criticality and outlines directions for future research, including physics-informed architectures, uncertainty quantification, and closed-loop integration with autonomous experimentation.
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Machine Learning (ML) techniques have emerged as a powerful tool in quantum matter research. In this poster, we highlight how ML algorithms enable us to analyze experimental data with unprecedented high sensitivities and identify topological phases even in the presence of unavoidable noises. To this end, we apply the trained network to low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions [1]. The obtained phase diagram by ML is consistent with the results obtained by using the conventional method on higher SNR data. Our work highlights the potential of machine learning techniques to be used in various quantum systems.