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 $N\ge 4$ 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.

arXiv comment20+4 pages, 15+3 figures

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• Spontaneously Broken Subsystem Symmetries
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Building models of topological quantum criticality from pivot Hamiltonians
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Boundary theory of the X-cube model in the continuum
• Fractionalization of subsystem symmetries in two dimensions
• Hybrid Symmetry Breaking in Classical Spin Models With Subsystem Symmetries
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet