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

• URL: http://arxiv.org/abs/2402.09520v2
• Date: Thu, 27 Jun 2024 17:01:07 GMT
• Title: Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Authors: Aswin Parayil Mana, Yabo Li, Hiroki Sukeno, Tzu-Chieh Wei,
• Abstract summary: We give an explicit operator representation of Kramers-Wannier duality transformation in higher-dimensional subsystem symmetric models. We construct the Kennedy-Tasaki transformation that maps subsystem symmetry-protected topological phases to spontaneous subsystem symmetry breaking phases.
• Score: 2.069923346979304
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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