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Condensed Matter > Statistical Mechanics
Title: From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
(Submitted on 27 Feb 2023 (v1), last revised 12 Mar 2024 (this version, v4))
Abstract: Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common to the XXZ spin chain and three other models: Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. The structure yields non-invertible maps between the four models while also guaranteeing all are integrable. We construct these maps explicitly utilising topological defects coming from fusion categories and the lattice version of the orbifold construction, and use them to give explicit conformal-field-theory partition functions describing their critical regions. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneous breaking of one in the former resulting in an unusual ground-state degeneracy.
Submission history
From: Paul Fendley [view email][v1] Mon, 27 Feb 2023 19:00:21 GMT (55kb,D)
[v2] Tue, 11 Apr 2023 17:36:21 GMT (242kb,D)
[v3] Wed, 9 Aug 2023 12:44:24 GMT (58kb,D)
[v4] Tue, 12 Mar 2024 18:04:23 GMT (59kb,D)
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