Dynamics of entanglement in a two-dimensional spin system

Qing Xu, Purdue University
Gehad Sadiek, Al Qasseem University; King Saud University; Ain Shams University
Sabre Kais, Birck Nanotechnology Center, Purdue University; Al Qasseem University; King Saud University

Date of this Version



Dynamics of entanglement in a two-dimensional spin system Qing Xu, Gehad Sadiek, and Sabre Kais Phys. Rev. A 83, 062312 – Published 10 June 2011


This is the published version of Qing Xu, Gehad Sadiek, and Sabre Kais. 10 June, 2011. Dynamics of entanglement in a two-dimensional spin system. First published in the Physical Review A and is available online at: https://doi.org/10.1103/PhysRevA.83.062312


We consider the time evolution of entanglement in a finite two-dimensional transverse Ising model. The model consists of a set of seven localized spin-1/2 particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction in the 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 rapid oscillations, the system shows great controllability under the effects 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 the exponential and hyperbolic forms, or the 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 is, the less distorted the entanglement profile is. Furthermore, the effect of thermal fluctuations is very devastating to the entanglement, which decays very rapidly as the temperature increases. Interestingly, although a large value of the magnetic field strength may yield a small entanglement, the magnetic field strength was found to be more persistent against thermal fluctuations than the small field strengths.


Nanoscience and Nanotechnology