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-$\frac{1}{2}$ 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 $\lambda =h/J$ in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $\lambda$ shows that the system exhibits a quantum phase transition at about ${\lambda }_c=3.01$, a transition induced by quantum fluctuations at the absolute zero of temperature.

• Received 22 September 2009

DOI:https://doi.org/10.1103/PhysRevA.81.022324