Universality of finite-size corrections to geometrical entanglement in one-dimensional quantum critical systems

• Published in: Journal of the Korean Physical Society Vol. 69; no. 7; pp. 1212 - 1218
• Main Authors: Liu, Xi-Jing, Hu, Bing-Quan, Cho, Sam Young, Zhou, Huan-Qiang, Shi, Qian-Qian
• Format: Journal Article
• Language: English
• Published: Seoul The Korean Physical Society 01.10.2016; Springer Nature B.V; 한국물리학회
• Subjects: Anisotropy; Boundary conditions; Mathematical and Computational Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Theoretical; 물리학; Spin chains; Affleck-Ludwig boundary entropy; Geometrical entanglements; One-dimensional critical systems
• ISSN: 0374-4884; 1976-8524
• DOI: 10.3938/jkps.69.1212

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 log 2 g min ) = −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.