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.

Information theoretical view of QCD effective model with heavy quarks

“…[25] for recent interesting criteria for the classification of the confinement-deconfinement crossover. The persistent homology is recently applied to the condensed matter physics and then it has been reported that the hidden order such as spin nematic ordering and spin liquids can be clarified from the persistent homology analysis [26]. Therefore, it seems to be interesting that we can utilize the information theoretic quantity to investigate the mysterious confinement-deconfinement nature of QCD.…”