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 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.
Keywords
GENERALIZED EIGENVALUE PROBLEM; QUANTUM; FIELD
DOI
10.1103/PhysRevA.81.022324
Citation
Qing Xu, Sabre Kais, Maxim Naumov, and Ahmed Sameh. Exact calculation of entanglement in a 19 -site two-dimensional spin system. Phys. Rev. A 81, 022324. https://doi.org/10.1103/PhysRevA.81.022324
Date of this Version
2-2010
Recommended Citation
Xu, Qing; Kais, Sabre; Naumov, Maxim; and Sameh, Ahmed, "Exact calculation of entanglement in a 19-site two-dimensional spin system" (2010). Birck and NCN Publications. Paper 651.
http://dx.doi.org/10.1103/PhysRevA.81.022324
Comments
This is the published version of Qing Xu, Sabre Kais, Maxim Naumov, and Ahmed Sameh. (23 February 2010). Exact calculation of entanglement in a 19 -site two-dimensional spin system. First published in the Physical Review A and is available online at: https://doi.org/10.1103/PhysRevA.81.022324