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Valence Bond Entanglement Entropy

Fabien Alet, Sylvain Capponi, Nicolas Laflorencie and Matthieu Mambrini

par Webmaster - 1er mars 2007

Selected for the Virtual Journal of Quantum Information, September 2007 Issue

Selected for the Virtual Journal of Nanoscale Science & Technology, September 2007 Issue

We introduce for SU(2) symmetric quantum spin systems the notion of Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, this quantity can be calculated via Quantum Monte Carlo simulations directly performed in the valence bond basis. We show that the Valence Bond Entanglement Entropy contains all features of the von Neumann entanglement entropy and offers, among others, the advantage of being computable in all dimensions. In one dimension, predictions for pure conformally invariant and infinite randomness fixed points are recovered. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and an area law with multiplicative logarithmic corrections for the Néel phase.