Correlation function diagnostics for type-I fracton phases

TL;DR

This paper introduces correlation function diagnostics for Type I fracton phases, linking them to classical Ising models with subsystem symmetries, and verifies these diagnostics through Monte Carlo simulations.

Contribution

It develops new correlation diagnostics for Type I fracton phases based on partial deconfinement and constructs their connection to classical Ising models with subsystem symmetries.

Findings

Correlation diagnostics successfully characterize Type I fracton phases.

Explicit construction of the spacetime partition function for the plaquette Ising model.

Monte Carlo simulations verify the theoretical predictions.

Abstract

Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting {\it partial deconfinement}. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations.