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 means to detect and quantitatively describe center vortices in $\mathrm{SU}(2)$ lattice gauge theory gauge-invariant manner. provide evidence for sensitivity our method by detecting vortex explicitly inserted using twisted boundary conditions deconfined phase. This inspires definition new phase indicator deconfinement transition. also construct without reference simple $k$-nearest neighbours classifier. Finite-size scaling analyses both persistence-based indicators yield accurate estimates critical $\beta$ exponent correlation length $\nu$