title: Valence bond entanglement entropy.
abstract: We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.
authors.affiliation: Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier, CNRS, 31062 Toulouse, France. alet@irsamc.ups-tlse.fr
authors.forename: Fabien
authors.initials: F
authors.lastname: Alet
authors.forename: Sylvain
authors.initials: S
authors.lastname: Capponi
authors.forename: Nicolas
authors.initials: N
authors.lastname: Laflorencie
authors.forename: Matthieu
authors.initials: M
authors.lastname: Mambrini