Asymptotic steady state of a dissipative long-range interacting spin system at finite temperature

Abstract

Many of the recently developed quantum systems that are considered promising candidates for the underlying technology of quantum computing enjoy long-range interaction, which is even tunable in some of them. Most of these systems can be described using the Heisenberg spin model to represent their interaction with the same system or a different one in hybrid structures. We consider here a finite two-dimensional spin system with a varying spin-spin long-range interaction under the effect of an external uniform magnetic field. We investigate the dynamics of the system and its asymptotic behavior at different degrees of anisotropy and interaction range under coupling to a thermal dissipative environment, starting from different initial states. We show that the system spin state and bipartite entanglement evolve in time to reach asymptotic values that are enhanced significantly by the degree of anisotropy and interaction range, whereas the thermal dissipative environment degrades the entanglement asymptotic equilibrium value as the temperature increases. Interestingly, while the robustness of the spin system against the environment’s thermal dissipative effects increases with the interaction range and degree of anisotropy, the entanglement between the far sites on the lattice shows its highest resilience in the partially anisotropic system, which might be attributed to a critical behavior taking place in the system. While the system’s early dynamics varies significantly depending on the initial state, the asymptotic equilibrium value is found to be completely independent.