Fractal Subsystem Symmetries, 't Hooft Anomalies, and UV/IR Mixing

Abstract

In this work, we study unconventional anisotropic topologically ordered phases in $3d$ that manifest type-II fractonic physics along submanifolds. While they behave as usual topological order along a preferred spatial direction, their physics along perpendicular planes is dictated by the presence of fractal subsystem symmetries, completely restricting the mobility of anyonic excitations and their bound states. We consider an explicit lattice model realization of such phases and proceed to study their properties under periodic boundary conditions and, later, in the presence of boundaries. We find that for specific lattice sizes, the system possesses line and fractal membrane symmetries that are mutually anomalous, resulting in a nontrivially gapped ground state space. This amounts to the spontaneous breaking of the fractal symmetries, implying a subextensive ground state degeneracy. For the remaining system sizes the fractal symmetries are explicitly broken by the periodic boundary conditions, which is intrinsically related to the uniqueness of the ground state. Despite that, the system is still topologically ordered since locally created quasiparticles have nontrivial mutual statistics and, in the presence of boundaries, it still presents anomalous edge modes. The intricate symmetry interplay dictated by the lattice size is a wild manifestation of ultraviolet/infrared (UV/IR) mixing.

8+6 pages, 5+6 figures, clarifications added, typos fixed, refs. added, v2 matches published version

References in corpus (19)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Generalized Symmetries in Condensed Matter
• Fracton Phases of Matter
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• An Introduction to Higher-Form Symmetries
• Fracton phases via exotic higher-form symmetry-breaking
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Exact emergent higher-form symmetries in bosonic lattice models
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Rank-2 Toric Code in Two Dimensions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Fracton Self-Statistics
• Lattice Clifford fractons and their Chern-Simons-like theory
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Pascal's Triangle Fractal Symmetries
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model

Cited by in corpus (4)

• Fractal Subsystem Symmetries, Anomalies, Boundaries, and Effective Field Theory
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes