Quantum synchronization between two spin chains using pseudo-bosonic equivalence

TL;DR

This paper demonstrates how two finite spin-1/2 chains can achieve classical and quantum synchronization through a novel pseudo-bosonic approach, revealing robustness against parameter variations and thermal noise.

Contribution

It introduces a new method using Holstein-Primakoff transformation to analyze quantum synchronization in spin chains as pseudo-bosonic systems.

Findings

Achieves classical and perfect quantum synchronization under optimal conditions

Synchronization is robust against changes in spin number and coupling

Thermal noise can affect the synchronization quality

Abstract

Quantum synchronization among many spins is an intriguing domain of research. In this paper, we explore the quantum synchronization of two finite chains of spin-1/2 particles, via a nonlinear interaction mediated by a a central intermediary spin chain. We introduce a novel approach using the Holstein-Primakoff transformation to treat the spin chains as pseudo-bosonic systems and thereby applying the synchronization criteria for harmonic oscillators. Our theoretical framework and numerical simulations reveal that under optimal conditions, the spin chains can achieve both classical and perfect quantum synchronization. We show that quantum synchronization is robust against variations in the number of spins and inter-spin coupling, though may be affected by thermal noise. This work advances the understanding of synchronization in multi-spin systems and introduces a generalized synchronization measure for both bosons and fermions.