Entanglement and Density Matrix of a Block of Spins in AKLT Model

We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\ln(S+1)^{2}$.Comment: Revised version, typos corrected, references added, 31 page

Diffusional and vibrational properties of water confined in very thin nanoporous glasses probed by light and neutron scattering

Rayleigh-wing, Raman and quasi-elastic neutron scattering data on water confined into nanoporous glasses (silica 26 Å pores), are presented and discussed. The H-bond among water molecules and Si-OH surface groups originates strong hydration effects, that induce more stable structural environments in which the memory of collective modes (the [Math]60 cm-1 and [Math]190 cm-1 shoulders due to the HB bending and HB stretching modes of water) is lost and the O-H stretching band connected to low-density water tends to disappear. The quasi-elastic neutron response is explained in terms of two available current models : the Dianoux-Volino model and the MCT model