Higgs mechanism in higher-rank symmetric U(1) gauge theories

Subdimensional motion occurs when excitations of a system can only move in a lower-dimensional subspace of the full system. This phenomenon occurs both in a class of generalized U(1) gauge theories and in ``fracton'' phases found in certain exactly solvable gapped spin models. Here, the authors present and analyze a more general class of symmetric higher-rank U(1) gauge theories and show how these two cases of subdimensional motion are connected via the Higgs mechanism, which often yields conventional phases but in special cases can drive a symmetric higher-rank U(1) gauge theory into a fracton phase.