Finding hidden order in spin models with persistent homology

TL;DR

This paper introduces a novel application of persistent homology to identify and visualize phases, including hidden orders, in spin models by converting configurations into barcodes and using dimensionality reduction.

Contribution

It demonstrates that persistent homology can serve as a universal framework for detecting phases and hidden orders in spin models, providing visual insights into configuration space.

Findings

Persistent homology successfully identifies phases in spin models.

Barcodes provide a descriptive visualization of configuration space.

Dimensionality reduction reveals phase diagrams clearly.

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.