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arXiv · 1901.08285

A Defect Verlinde Formula

Ce Shen·Ling-Yan Hung
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Abstract

We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula that relates the fusion rules of the boundary excitations, and the "half-linking" number between condensed anyons and confined boundary excitations. This formula is a direct analogue of the Verlinde formula. We also demonstrate how these half-linking numbers can be computed in explicit Abelian and non-Abelian examples. As a fundamental property of topological orders and their allowed boundaries, this should also find applications in finding suitable platforms realizing quantum computing devices.

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Ce Shen, Ling-Yan Hung. 2019-01-24. A Defect Verlinde Formula. https://doi.org/10.1103/physrevlett.123.051602

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