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

TL;DR

This paper develops a unifying algebraic framework based on fusion-category defects and lattice orbifolds to relate four integrable lattice models: the XXZ spin chain, a Rydberg-blockade ladder, a three-state antiferromagnet, and two Ising zigzag chains. By embedding these models in a shared so(3)_2/BMW/chromatic-algebra structure, it constructs explicit non-invertible duality maps that link their spectra and partition functions, and proves a commutative square of maps linking all four systems. The authors derive exact continuum limits via orbifold conformal field theories, producing precise partition-function relations and identifying non-invertible symmetries, including a self-duality that is spontaneously broken in the Rydberg ladder. These results reveal deep structural connections among seemingly different quantum many-body systems and demonstrate how categorical methods yield concrete, testable predictions for integrable lattice models and their CFT counterparts. The framework provides a blueprint for discovering further non-invertible dualities in low-dimensional quantum systems and for understanding the role of topological defects in organizing spectra across models.

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.