Topological quantum synchronization of fractionalized spins

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.

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• Synchronization in complex networks
• Quantum synchronization of two Van der Pol oscillators
• Mutual information as an order parameter for quantum synchronization
• Optical one-way quantum computing with a simulated valence-bond solid
• Oscillation collapse in coupled quantum van der Pol oscillators
• Quantum Synchronization in quadratically coupled quantum van der Pol oscillators
• Secure and efficient synchronization scheme for quantum key distribution
• Measurement-Induced Quantum Synchronization and Multiplexing
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model

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• Auxiliary-state facilitated phase synchronization phenomena in isolated spin systems
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