Dynamics of entanglement in a two-dimensional spin system

Abstract

We consider the time evolution of entanglement in a finite two dimensional transverse Ising model. The model consists of a set of 7 localized spin-1/2 particles in a two dimensional triangular lattice coupled through nearest neighbor exchange interaction in presence of an external time dependent magnetic field. The magnetic field is applied in different function forms: step, exponential, hyperbolic and periodic. We found that the time evolution of the entanglement shows an ergodic behavior under the effect of the time dependent magnetic fields. Also we found that while the step magnetic field causes great disturbance to the system creating rabid oscillations, the system shows great controllability under the effect of the other magnetic fields where the entanglement profile follows closely the shape of the applied field even with the same frequency for periodic fields. This follow up trend breaks down as the strength of the field, the transition constant for exponential and hyperbolic, or frequency for periodic field increase leading to rapid oscillations. We observed that the entanglement is very sensitive to the initial value of the applied periodic field, the smaller the initial value the less distorted is the entanglement profile. Furthermore, the effect of thermal fluctuations is very devastating to the entanglement which decays very rapidly as the temperature increases. Interestingly, although large value of the magnetic field strength may yield small entanglement, it was found to be more persistent against thermal fluctuations than the small field strengths.

References in corpus (5)

• Direct observation of quantum criticality in Ising spin chains
• Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field
• Entanglement Switch for Dipole Arrays
• Exact Calculation of Entanglement in a 19-site 2D Spin System
• Quantum anisotropic Heisenberg chains with superlattice structure: a DMRG study

Cited by in corpus (6)

• Manipulating entanglement sudden death in two coupled two-level atoms interacting off-resonance with a radiation field: an exact treatment
• Entanglement robustness in Heisenberg spin chains coupled to dissipative environment at finite temperature
• Tuning entanglement and ergodicity in two-dimensional spin systems using impurities and anisotropy
• Bipartite entanglement dynamics of two-level systems in sub-Ohmic reservoirs
• Asymptotic entanglement sudden death in two atoms with dipole-dipole and Ising interactions coupled to a radiation field at non-zero detuning
• Decoherence, relaxation and chaos in a kicked-spin ensemble