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Motivated by recent development in quantum entanglement, we study relationsamong concurrence $C$, SU$_q$(2) algebra, quantum phase transition andcorrelation length at the zero temperature for the XXZ chain. We find that atthe SU(2) point, the ground state possess the maximum concurrence. When theanisotropic parameter $\Delta$ is deformed, however, its value decreases. Itsdependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ in the XY metallicphase and near the critical point (i.e. $1<\Delta<1.3$) of the Ising-likeinsulating phase. We also study the dependence of $C$ on the correlation length$\xi$, and show that it satisfies $C=C_0-1/2\xi$ near the critical point. Fordifferent size of the system, we show that there exists a universal scalingfunction of $C$ with respect to the correlation length $\xi$.Comment: 4 pages, 3 figures. to appear in Phys. Rev.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Entanglement, quantum phase transition, and scaling in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XXZ</mml:mi></mml:math>chain

Entanglement, quantum phase transition, and scaling in theXXZchain