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

• URL: http://arxiv.org/abs/2310.09425v4
• Date: Thu, 13 Feb 2025 00:56:33 GMT
• Title: Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• Abstract summary: Some topological lattice models exhibit intricate lattice size dependence in their ground state degeneracy (GSD)<n>This and other features such as the position-dependent anyonic excitations are manifestations of UV/IR mixing.<n>Our work establishes the translation symmetry defect framework as a robust description of the UV/IR mixing in topological lattice models.
• Score: 0.7312229214872541
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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