Inter-Particle Correlations in the Dissipative Phase Transition of a Collective Spin Model

TL;DR

This study investigates interparticle correlations in a driven-dissipative collective spin model, revealing that entanglement peaks at the phase transition while quantum discord increases in the low-purity phase, highlighting complex quantum behaviors in open systems.

Contribution

It provides a detailed numerical analysis of quantum correlations in a collective spin model, emphasizing the distinct behaviors of entanglement and quantum discord across phase transitions.

Findings

Entanglement peaks at the phase transition point.

Quantum discord increases monotonically into the low-purity phase.

Entanglement persists near the transition despite open system effects.

Abstract

In open quantum systems undergoing phase transitions, the intricate interplay between unitary and dissipative processes leaves many information-theoretic properties opaque. We are here interested in interparticle correlations within such systems, specifically examining quantum entanglement, quantum discord, and classical correlation within the steady state of a driven-dissipative collective spin model. This model is renowned for, counterintuitively, its transition from a high-purity to a low-purity state with decreasing dissipation. Our investigation, rooted in numerical analysis using PPT criteria, underscores that entanglement reaches its zenith precisely at the phase transition juncture. Intriguingly, even within the mesoscopic scale near the transition point, entanglement endures across both phases, despite the open nature of the model. Notably, when employing traditional pairwise entanglement measures tailored to this model, detecting entanglement in the low-purity phase has proven elusive. In stark contrast, quantum discord and its variations chart an alternate trajectory, ascending monotonically as the system progresses into the low-purity phase. Consequently, lowered dissipation amplifies quantum correlation, yet it engenders entanglement solely in proximity to the transition point.