Entanglement, quantum phase transition and scaling in XXZ chain

Details Entanglement, quantum phase transition and scaling in XXZ chain Entanglement, quantum phase transition and scaling in XXZ chain

2003-07-18

arxiv.org/abs/quant-ph/0307131v2

Phys. Rev. A 68, 042330(2003)

Physics

Quantum Physics

4 pages, 3 figures. to appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.68.042330

Motivated by recent development in quantum entanglement, we study relations among concurrence $C$, SU$_q$(2) algebra, quantum phase transition and correlation length at the zero temperature for the XXZ chain. We find that at the SU(2) point, the ground state possess the maximum concurrence. When the anisotropic parameter $\Delta$ is deformed, however, its value decreases. Its dependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ in the XY metallic phase and near the critical point (i.e. $1<\Delta<1.3$) of the Ising-like insulating 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. For different size of the system, we show that there exists a universal scaling function of $C$ with respect to the correlation length $\xi$.

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