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

TL;DR

This paper uncovers a common algebraic structure linking the XXZ chain and three other models, revealing non-invertible dualities and symmetries that guarantee integrability and describe critical behavior.

Contribution

It introduces explicit non-invertible maps between these models using topological defects and fusion categories, advancing understanding of their integrability and critical phenomena.

Findings

Identifies a shared algebraic structure among four models.

Constructs explicit non-invertible duality maps using topological defects.

Describes critical regions with conformal-field-theory partition functions.

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.