M A Martín-Delgado | PubMed Health

PubMed2004

Diverging entanglement length in gapped quantum spin systems.

We prove the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length. Using the concept of entanglement swapping, the localizable entanglement is calculated exactly for valence bond and finitely correlated states, and the existence of the so-called string-order parameter is discussed. We also report on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.

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PubMed2003

Anderson transition in low-dimensional disordered systems driven by long-range nonrandom hopping.

The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically, using a supersymmetric method combined with a renormalization group analysis, as well as numerically that extended states may occur in the one- and two-dimensional Anderson model with a nonrandom hopping falling off as some power of the distance between sites. The different size scaling of the bare level spacing and the renormalized magnitude of the disorder seen by the quasiparticles finally results in the delocalization of states at one of the band edges of the quasiparticle energy spectrum.

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