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

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.

27 pages, 10 figures, Revised manuscript published in PRB

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