Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory

Abstract

This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II fracton physics dictated by a fractal subsystem symmetry. We obtain an expression for the ground state degeneracy, which depends intricately on the sizes of the plane, signaling a strong manifestation of ultraviolet/infrared (UV/IR) mixing. The ground state degeneracy can be interpreted in terms of spontaneous/explicit breaking of fractal subsystem symmetries. We also study the boundary physics, which in turn is useful to understand the connection with certain two-dimensional phases. Finally, we derive a low-energy but not long-distance effective field theory, by Higgsing a fractal $U(1)$ symmetry and taking the deep IR limit. This description embodies in a natural way several aspects of the phases, such as the content of generalized global symmetries, the role of fractal symmetries on the mobility of excitations, the anomalies, and the boundary physics.

58 pages, 30 figures, clarifications added, typos fixed, refs. added, v2 matches published version

References in corpus (15)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Generalized Symmetries in Condensed Matter
• Lecture Notes on Generalized Symmetries and Applications
• Anomaly Inflow for Subsystem Symmetries
• An Introduction to Higher-Form Symmetries
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Fracton Self-Statistics
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• Anomaly inflow for dipole symmetry and higher form foliated field theories
• Fractal Nodal Band Structures
• Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing

Cited by in corpus (4)

• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Systematic construction of stabilizer codes via gauging abelian boundary symmetries
• Matrix product state classification of 1D multipole symmetry protected topological phases