Subdimensional criticality: Condensation of lineons and planons in the X-cube model

Abstract

We study quantum phase transitions out of the fracton ordered phase of the $\mathbb{Z}_N$ X-cube model. These phase transitions occur when various types of sub-dimensional excitations and their composites are condensed. The condensed phases are either trivial paramagnets, or are built from stacks of $d=2$ or $d=3$ deconfined gauge theories, where $d$ is the spatial dimension. The nature of the phase transitions depends on the excitations being condensed. Upon condensing dipolar bound states of fractons or lineons, for $N \geq 4$ we find stable critical points described by decoupled stacks of $d=2$ conformal field theories. Upon condensing lineon excitations, when $N > 4$ we find a gapless phase intermediate between the X-cube and condensed phases, described as an array of $d=1$ conformal field theories. In all these cases, effective subsystem symmetries arise from the mobility constraints on the excitations of the X-cube phase and play an important role in the analysis of the phase transitions.