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arXiv · 2402.09520

Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension

Aswin Parayil Mana·Yabo Li·Hiroki Sukeno·Tzu-Chieh Wei
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Abstract

We give an explicit operator representation (via a sequential circuit and projection to symmetry subspaces) of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models generalizing the construction in the 1D transverse-field Ising model. Using the Kramers-Wannier duality operator, we also construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases, where the symmetry group for the former is either $\mathbb{Z}_2\times\mathbb{Z}_2$ or $\mathbb{Z}_2$. This generalizes the recently proposed picture of one-dimensional Kennedy-Tasaki transformation as a composition of manipulations involving gauging and stacking symmetry-protected topological phases to higher dimensions.

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Aswin Parayil Mana, Yabo Li, Hiroki Sukeno, Tzu-Chieh Wei. 2024-02-14. Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension. https://doi.org/10.1103/physrevb.109.245129

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