Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model

TL;DR

This paper investigates the nature of string order and hidden symmetry breaking in the q-deformed AKLT model, proposing a new non-local transformation to better understand the model's symmetry properties.

Contribution

It introduces a modified non-local transformation based on a recent generalization of Witten's Conjugation, improving the description of symmetry breaking in the q-deformed AKLT model.

Findings

The original Kennedy-Tasaki duality leads to a non-local Hamiltonian.

The new transformation better captures the symmetry breaking.

The approach clarifies the role of hidden symmetries in the model.

Abstract

We revisit the question of string order and hidden symmetry breaking in the q-deformed AKLT model, an example of a spin chain that possesses generalized symmetry. We first argue that the non-local Kennedy-Tasaki duality transformation that was previously proposed to relate the string order to a local order parameter leads to a non-local Hamiltonian and thus does not provide a physically adequate description of the symmetry breaking. We then present a modified non-local transformation which is based on a recently developed generalization of Witten's Conjugation to frustration-free lattice models and capable of resolving this issue.