Finding hidden order in spin models with persistent homology
Bart Olsthoorn, Johan Hellsvik, Alexander V. Balatsky · Physical Review Research · 2020
Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data.In this paper, we demonstrate that PH can be used as a universal framework to identify phases of classical spins on a lattice.This demonstration includes 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.