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.
@article{arxiv.2009.05141,
title = {Finding hidden order in spin models with persistent homology},
author = {Bart Olsthoorn and Johan Hellsvik and Alexander V. Balatsky},
journal= {arXiv preprint arXiv:2009.05141},
year = {2020}
}