Universality of finite-size corrections to geometrical entanglement in one-dimensional quantum critical systems
Universality of finite-size corrections to geometrical entanglement in one-dimensional quantum critical systems
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DOI：
10.3938/jkps.69.1212
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发表时间：
2016-10
影响因子：
0.6
通讯作者：
Xi-Jing Liu;Bing Hu;Sam Young Cho;Huan-Qiang Zhou;Q. Shi
中科院分区：
文献类型：
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作者：
Xi-Jing Liu;Bing Hu;Sam Young Cho;Huan-Qiang Zhou;Q. Shi
最近，在自旋为1/2的链中，对每个晶格位置的几何纠缠的有限尺寸修正已经被数值地显示为与系统尺寸成反比，并且它的前因子B已经被建议为可能是普适的[Q-Q]。Shi等人，12，025008（2010）]。作为其普适性的可能证据，前因子的数值已经通过使用具有Neumann边界条件的自由紧致化场的Affleck-Ludwig边界熵解析地确认[J-M. Stephan等人，Phys. Rev. B 82，180406（R）（2010）]。然而，阿弗莱克-路德维希边界熵是不唯一的，并依赖于共形不变的边界条件。在这里，我们证明了存在唯一的对应于对每个格点的几何纠缠的有限尺寸修正的Affleck-Ludwig边界熵，并证明了对于具有单离子各向异性的自旋为1的XXZ系统的任何临界区域，前因子B与Affleck-Ludwig边界熵的相应最小基态简并度gmin的比值是常数，即，B/（2 log2gmin）= −1。以前研究的自旋为1/2的系统，包括量子三态Potts模型，已经验证了普适比。因此，对每个格点的几何纠缠及其前因子B的逆有限尺寸修正对于一维临界系统是通用的。
Recently, the finite-size corrections to the geometrical entanglement per lattice site in the spin-1/2 chain have been numerically shown to scale inversely with system size, and its prefactor b has been suggested to be possibly universal [Q-Q. Shi et al., New J. Phys. 12, 025008 (2010)]. As possible evidence of its universality, the numerical values of the prefactors have been confirmed analytically by using the Affleck-Ludwig boundary entropy with a Neumann boundary condition for a free compactified field [J-M. Stephan et al., Phys. Rev. B 82, 180406(R) (2010)]. However, the Affleck-Ludwig boundary entropy is not unique and does depend on conformally invariant boundary conditions. Here, we show that a unique Affleck-Ludwig boundary entropy corresponding to a finitesize correction to the geometrical entanglement per lattice site exists and show that the ratio of the prefactor b to the corresponding minimum groundstate degeneracy gmin for the Affleck- Ludwig boundary entropy is a constant for any critical region of the spin-1 XXZ system with the single-ion anisotropy, i.e., b/(2 log2gmin) = −1. Previously studied spin-1/2 systems, including the quantum three-state Potts model, have verified the universal ratio. Hence, the inverse finite-size correction to the geometrical entanglement per lattice site and its prefactor b are universal for one-dimensional critical systems.