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.

arXiv comment58 pages, 30 figures, clarifications added, typos fixed, refs. added, v2 matches published version

References in corpus (36)

• Generalized Global Symmetries
• Zoo of quantum-topological phases of matter
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Generalized Symmetries in Condensed Matter
• Fracton Phases of Matter
• A symmetry principle for Topological Quantum Order
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Exotic topological order in fractal spin liquids
• Design and characterization of electronic fractals
• Topological order in an exactly solvable 3D spin model
• Glassy quantum dynamics in translation invariant fracton models
• Glassy dynamics and aging in an exactly solvable spin model
• Emergent (anomalous) higher symmetries from topological orders and from dynamical electromagnetic field in condensed matter systems
• Topological Quantum Glassiness
• Fractal Symmetric Phases of Matter
• Lecture Notes on Generalized Symmetries and Applications
• Topological states on fractal lattices
• Universal quantum computation using fractal symmetry-protected cluster phases
• Anomaly Inflow for Subsystem Symmetries
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• An Introduction to Higher-Form Symmetries
• Fracton phases via exotic higher-form symmetry-breaking
• 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
• A degeneracy bound for homogeneous topological order
• 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