Exact Calculation of Entanglement in a 19-site 2D Spin System
Abstract
Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-1/2 particles in a two dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of shows that the system exhibits a quantum phase transition at about = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.
Keywords
Cite
@article{arxiv.0909.4764,
title = {Exact Calculation of Entanglement in a 19-site 2D Spin System},
author = {Qing Xu and Sabre Kais and Maxim Naumov and Ahmed Sameh},
journal= {arXiv preprint arXiv:0909.4764},
year = {2011}
}