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

TL;DR

This paper investigates UV/IR mixing in topological lattice models through topological entanglement entropy calculations, revealing how translation symmetry defects explain size-dependent ground state degeneracy and excitations.

Contribution

It provides an exact TEE calculation for the rank-2 toric code and introduces a translation symmetry defect framework to explain UV/IR mixing phenomena.

Findings

TEE for contractible boundaries is size-independent

TEE for non-contractible boundaries depends on lattice size

Translation symmetry defects explain GSD and TEE size dependence

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.