Partenaires

CNRS
UPS



Rechercher

Sur ce site

Sur le Web du CNRS


Accueil du site > Publications > Publications 2010 > Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies

Geometric entanglement of critical XXZ and Ising chains and Affleck-Ludwig boundary entropies

Jean-Marie Stéphan, Grégoire Misguich, Fabien Alet

par Webmaster - 26 juillet 2010

We study the geometrical entanglement of the XXZ chain in its critical regime. Recent numerical simulations [Q.-Q. Shi, R. Orus, J. O. Fjaerestad and H.-Q Zhou, New J. Phys. 12, 025008 (2010)] indicate that it scales linearly with system size, and that the first subleading correction is constant, which was argued to be possibly universal. In this work, we confirm the universality of this number, by relating it to the Affleck-Ludwig boundary entropy corresponding to a Neumann boundary condition for a free compactified field. We find that the subleading constant is a simple function of the compactification radius, in agreement with the numerics. As a further check, we compute it exactly on the lattice at the XX point. We also discuss the case of the Ising chain in transverse field and show that the geometrical entanglement is related to the Affleck-Ludwig boundary entropy associated to a ferromagnetic boundary condition.

Phys. Rev. B 82, 180406(R) (2010), arXiv:1007.4161