From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects

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 find an algebraic structure in the XXZ spin chain and three other Hamiltonians that yields non-invertible maps between them and also guarantees all are integrable. The other models describe Rydberg-blockade bosons with one particle per square of a ladder, a three-state antiferromagnet, and two Ising chains coupled in a zigzag fashion. We construct the non-invertible maps explicitly by using topological defects coming from fusion categories and the lattice version of the orbifold construction. The Rydberg and Ising ladders also possess interesting non-invertible symmetries, with the spontaneously breaking of one in the former resulting in an unusual ground-state degeneracy. We give explicit conformal-field-theory partition functions describing their critical regions, and provide a detailed correspondence between lattice and continuum operators in the integrable Rydberg-blockade ladder.

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