Non-Invertible Duality Transformation Between SPT and SSB Phases

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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Cited by in corpus (59)

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• Universal entanglement spectrum in gapless symmetry protected topological states
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• Intrinsically/Purely Gapless-SPT from Non-Invertible Duality Transformations
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
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• Gauging non-invertible symmetries on the lattice
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• Boundary SymTFT
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• Higher-order topological phases protected by noninvertible and subsystem symmetries
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• Boundary critical phenomena in the quantum Ashkin-Teller model