Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy

Abstract

Some topological lattice models in two spatial dimensions exhibit intricate lattice size dependence in their ground state degeneracy (GSD). This and other features such as the position-dependent anyonic excitations are manifestations of UV/IR mixing. In the first part of this paper, we perform an exact calculation of the topological entanglement entropy (TEE) for a specific model, the rank-2 toric code. This analysis includes both contractible and non-contractible boundaries, with the minimum entropy states identified specifically for non-contractible boundaries. Our results show that TEE for a contractible boundary remains independent of lattice size, whereas TEE for non-contractible boundaries, similarly to the GSD, shows intricate lattice-size dependence. In the latter part of the paper we focus on the fact that the rank-2 toric code is an example of a translation symmetry-enriched topological phase, and show that viewing distinct lattice size as a consequence of different translation symmetry defects can explain both our TEE results and the GSD of the rank-2 toric code. Our work establishes the translation symmetry defect framework as a robust description of the UV/IR mixing in topological lattice models.

17 pages, 6 figures

References in corpus (18)

• A classification of symmetry enriched topological phases with exactly solvable models
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Characterizing topological order by studying the ground states of an infinite cylinder
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Rank-2 Toric Code in Two Dimensions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Symmetric higher rank topological phases on generic graphs
• Anyon condensation web and multipartite entanglement in 2D modulated gauge theories
• Topological order and Fractons from Gauging Exponential Symmetries
• Entanglement entropy of higher rank topological phases

Cited by in corpus (5)

• Topological order and Fractons from Gauging Exponential Symmetries
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes