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Exact Calculation of Entanglement in a 19-site 2D 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 $λ$ = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $λ$ shows that the system exhibits a quantum phase transition at about $λ_c$ = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.