Article
Unsupervised machine learning account of magnetic transitions in the Hubbard model
Physical Review E
(2018)
Abstract
We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the “sign problem” in quantum Monte Carlo simulations is present.
Keywords
- Antiferromagnetism,
- Magnetic phase transitions,
- Hubbard model,
- Lattice models in condensed matter,
- Machine learning,
- Quantum Monte Carlo
Disciplines
Publication Date
January, 2018
DOI
10.1103/PhysRevE.97.013306
Publisher Statement
This article originally appeared in Physical Review E, volume 97, issue 1, 2018, published by the American Physical Society. ©2018 American Physical Society. The article can also be found online at this link.
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Citation Information
Kelvin Ch'ng, Nick Vazquez and Ehsan Khatami. "Unsupervised machine learning account of magnetic transitions in the Hubbard model" Physical Review E Vol. 97 Iss. 1 (2018) ISSN: 2470-0045 Available at: http://works.bepress.com/ehsan_khatami/40/