Finding hidden order in spin models with persistent homology
Bart Olsthoorn, Johan Hellsvik, Alexander V. Balatsky
Abstract
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.
Topics & Concepts
Persistent homologySpinsVisualizationCurse of dimensionalityMathematicsSpin (aerodynamics)Homology (biology)Topological data analysisBarcodePhysicsPhase spaceSpace (punctuation)Field (mathematics)Dimensionality reductionComputer scienceTheoretical physicsSequence (biology)Order (exchange)Topology (electrical circuits)Statistical physicsAlgorithmTopological and Geometric Data AnalysisTheoretical and Computational PhysicsHomotopy and Cohomology in Algebraic Topology