Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions

Abstract

Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form subsystem symmetries, which allow us to adapt tools from the study of conventional topological phases to the fracton setting. We demonstrate that certain transitions out of familiar fracton phases, including the X-cube model, can be understood in terms of the spontaneous breaking of higher-form subsystem symmetries. We find simple pictures for these seemingly complicated fracton topological phase transitions by relating them in an exact manner, via gauging, to spontaneous higher-form subsystem symmetry breaking phase transitions of decoupled stacks of lower-dimensional models. We harness this perspective to construct a sequence of unconventional subdimensional critical points in two and three spatial dimensions based on the stacking and gauging of canonical models with higher-form symmetry. Through numerous examples, we illustrate the ubiquity of coupled layer constructions in theories with higher-form subsystem symmetries.

128 pages, 8 tables, 13 figures, minor typos corrected in v2, to appear in SciPost Physics

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• A symmetry principle for gauge theories with fractons
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• Deep learning lattice gauge theories
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing
• Protocols for Creating Anyons and Defects via Gauging
• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Ground state properties of the Heisenberg-compass model on the square lattice
• Subsystem Symmetry Fractionalization and Foliated Field Theory
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Fractonic criticality in Rydberg atom arrays
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
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• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Relaxation and fluctuations of a mass- and dipole-conserving stochastic lattice gas
• Emergent criticality in a constrained boson model