Exact calculation of entanglement in a 19-site two-dimensional spin system

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 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.