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

TL;DR

This paper investigates quantum phase transitions in the X-cube fracton model, revealing how condensation of various excitations leads to distinct critical points and phases characterized by conformal field theories and subsystem symmetries.

Contribution

It provides a detailed analysis of phase transitions involving sub-dimensional excitations in the X-cube model, identifying new stable critical points and intermediate gapless phases.

Findings

Condensation of dipolar bound states yields decoupled 2D conformal field theories.

Lineon condensation leads to an intermediate gapless phase with 1D conformal field theories.

Subsystem symmetries emerge from excitation mobility constraints and influence phase transition behavior.

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.