Entanglement in a simple quantum phase transition

Osborne, Tobias J. and Nielsen, Michael A. (2002) Entanglement in a simple quantum phase transition. Physical Review A, 66 3: 032110-1-032110-14. doi:10.1103/PhysRevA.66.032110

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Author Osborne, Tobias J.
Nielsen, Michael A.
Title Entanglement in a simple quantum phase transition
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2002-09-23
Sub-type Article (original research)
DOI 10.1103/PhysRevA.66.032110
Open Access Status File (Publisher version)
Volume 66
Issue 3
Start page 032110-1
End page 032110-14
Total pages 14
Place of publication United States
Publisher American Physical Society
Collection year 2002
Language eng
Abstract What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.
Keyword Quantum phase transitions
Quantum information
Quantum systems
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
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Created: Wed, 04 Apr 2007, 16:51:53 EST by Kaye Eldridge on behalf of School of Mathematics & Physics