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 论文
摘要
Motivated by recent development in quantum entanglement, we study relations among concurrence C, ${\mathrm{SU}}_{q}(2)$ algebra, quantum phase transition and correlation length at the zero temperature for the $\mathrm{XXZ}$ chain. We find that at the SU(2) point, the ground state possesses the maximum concurrence. When the anisotropic parameter $\ensuremath{\Delta}$ is deformed, however, its value decreases. Its dependence on $\ensuremath{\Delta}$ scales as ${C=C}_{0}\ensuremath{-}{C}_{1}(\ensuremath{\Delta}\ensuremath{-}{1)}^{2}$ in the $\mathrm{XY}$ metallic phase and near the critical point (i.e., $1<\ensuremath{\Delta}<1.3)$ of the Ising-like insulating phase. We also study the dependence of C on the correlation length $\ensuremath{\xi},$ and show that it satisfies ${C=C}_{0}\ensuremath{-}1/2\ensuremath{\xi}$ near the critical point. For different sizes of the system, we show that there exists a universal scaling function of C with respect to the correlation length $\ensuremath{\xi}.$