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arXiv · 2301.07899

Non-Invertible Duality Transformation Between SPT and SSB Phases

Linhao Li·Masaki Oshikawa·Yunqin Zheng
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Abstract

In 1992, Kennedy and Tasaki constructed a non-local unitary transformation that maps between a $\mathbb{Z}_2\times \mathbb{Z}_2$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical Symmetry-Protected Topological phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain, by sacrificing unitarity. The operator realizing such a non-unitary transformation satisfies non-invertible fusion rule, and implements a generalized gauging of the $\mathbb{Z}_2\times \mathbb{Z}_2$ global symmetry. These findings connect the Kennedy-Tasaki transformation to numerous other concepts developed for SPT phases, and opens a way to construct SPT phases systematically using the duality mapping.

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Linhao Li, Masaki Oshikawa, Yunqin Zheng. 2023-01-19. Non-Invertible Duality Transformation Between SPT and SSB Phases. https://doi.org/10.1103/physrevb.108.214429

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