Topological quantum synchronization of fractionalized spins

TL;DR

This paper demonstrates topological quantum synchronization of fractionalized spins in the AKLT model, showing robustness due to topological protection and independence from permutation symmetries.

Contribution

It introduces a method to synchronize fractionalized spins using dissipators in a topologically protected system, highlighting robustness and independence from permutation symmetry.

Findings

Synchronization achieved via global spin-lowering dissipator

Robustness of synchronization within the Haldane-gap phase

Topological protection enables synchronization without permutation symmetry

Abstract

The gapped symmetric phase of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model exhibits fractionalized spins at the ends of an open chain. We show that breaking SU(2) symmetry and applying a global spin-lowering dissipator achieves synchronization of these fractionalized spins. Additional local dissipators ensure convergence to the ground state manifold. In order to understand which aspects of this synchronization are robust within the entire Haldane-gap phase, we reduce the biquadratic term which eliminates the need for an external field but destabilizes synchronization. Within the ground state subspace, stability is regained using only the global lowering dissipator. These results demonstrate that fractionalized degrees of freedom can be synchronized in extended systems with a significant degree of robustness arising from topological protection. \rev{A direct consequence is that permutation symmetries are not required for the dynamics to be synchronized, representing a clear advantage of topological synchronization compared to synchronization induced by permutation symmetries.