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

Qing Xu, Sabre Kais, Maxim Naumov, Ahmed Sameh

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14 Citations (Scopus)


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-12 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 λc=3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.

Original languageEnglish
Article number022324
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 23 Feb 2010
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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