Probing center vortices and deconfinement in SU(2) lattice gauge theory with persistent homology

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in SU(2) lattice gauge theory in a gauge-invariant manner. We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase. This inspires the definition of a new phase indicator for the deconfinement phase transition. We also construct a phase indicator without reference to twisted boundary conditions using a simple k-nearest-neighbors classifier. Finite-size scaling analyses of both persistence-based indicators yield accurate estimates of the critical beta and critical exponent of correlation length nu of the deconfinement phase transition.

Automated summary

We study the use of persistent homology as a tool to detect and describe center vortices in the SU(2) lattice gauge theory. We show evidence of the sensitivity of our method by detecting explicitly inserted vortices using twisted boundary conditions. We propose a new phase indicator for the deconfinement phase transition and construct another indicator without reference to twisted boundary conditions. Finite-size scaling analyses of both indicators provide accurate estimates of the critical beta and critical exponent of the deconfinement phase transition.