Finding hidden order in spin models with persistent homology

Abstract

Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models, including hidden order such as spin nematic ordering and spin liquids. By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram.

arXiv comment8 pages, 6 figures

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• Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology
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• Unsupervised machine learning approaches to the $q$-state Potts model
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• Confinement in non-Abelian lattice gauge theory via persistent homology
• Unsupervised Interpretable Learning of Phases From Many-Qubit Systems
• Probing universal dynamics with topological data analysis in a gluonic plasma
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• Detecting defect dynamics in relativistic field theories far from equilibrium using topological data analysis
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Information theoretical view of QCD effective model with heavy quarks
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• Topological data analysis of the deconfinement transition in SU(3) lattice gauge theory