### 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-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 language | English |
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Article number | 022324 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 81 |

Issue number | 2 |

DOIs | |

Publication status | Published - 23 Feb 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*81*(2), [022324]. https://doi.org/10.1103/PhysRevA.81.022324

**Exact calculation of entanglement in a 19-site two-dimensional spin system.** / Xu, Qing; Kais, Sabre; Naumov, Maxim; Sameh, Ahmed.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 81, no. 2, 022324. https://doi.org/10.1103/PhysRevA.81.022324

}

TY - JOUR

T1 - Exact calculation of entanglement in a 19-site two-dimensional spin system

AU - Xu, Qing

AU - Kais, Sabre

AU - Naumov, Maxim

AU - Sameh, Ahmed

PY - 2010/2/23

Y1 - 2010/2/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77249122201&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77249122201&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.81.022324

DO - 10.1103/PhysRevA.81.022324

M3 - Article

VL - 81

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022324

ER -