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arXiv · 2108.05730

Galois conjugates of String-net Model

Chao-Yi Chen·Bing-Xin Lao·Xin-Yang Yu·Ling-Yan Hung
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Abstract

We revisit a class of non-Hermitian topological models that are Galois conjugates of their Hermitian counter parts. Particularly, these are Galois conjugates of unitary string-net models. We demonstrate these models necessarily have real spectra, and that topological numbers are recovered as matrix elements of operators evaluated in appropriate bi-orthogonal basis, that we conveniently reformulate as a concomitant Hilbert space here. We also compute in the bi-orthogonal basis thetopological entanglement entropy, demonstrating that its real part is related to the quantum dimension of the topological order. While we focus mostly on the Yang-Lee model, the results in the paper apply generally to Galois conjugates.

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Chao-Yi Chen, Bing-Xin Lao, Xin-Yang Yu, Ling-Yan Hung. 2021-08-12. Galois conjugates of String-net Model. https://doi.org/10.1103/physrevd.105.065009

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