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 . 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 . NSF Grant DMS-0503712.     

The most general L operator for the R-matrix of the XXX model

The problem of describing all the monodromy matrices for R matrices of the XXX and XXZ models is discussed. It is shown that the L operator of the lattice nonlinear Schrödinger model generates all possible monodromy matrices for the XXX R matrix.     

Temperature correlation functions in the XX0 Heisenberg chain. I

Space and time dependent correlation functions in the Heisenberg XX0 chain (in the transverse magnetic field) are expressed in terms of Fredholm determinants of linear integral operators. This is done in order to evaluate asymptotics of these correlations, which we shall do in next paper.I.N.F.N., Sezione di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy. Forum: Project on Condensed Matter Theory of INFM, Firenze-Pisa, Italy and Laboratoire de Physique Théorique ENSLAPP, Ecole Normale Superieure de Lyon, France, Permanent Address: Sankt-Petersburg Branch (POMI) of V.A. Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191011 St.-Petersburg, Russia. Institute for Theoretical Physics, State University of New York at Stony Brook, NY 11794-3840, USA. Dipartimento di Fisica, Università di Firenze, Largo E. Fermi 2, 50125 Firenze, Italy. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 19–51, January, 1993.     

Determinant representation for correlation functions of spin-1/2 XXX and XXZ Heisenberg magnets

We consider zero temperature correlation functions of the spin-1/2 XXZ Heisenberg chain in the critical regime –1<1 in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in term of determinats of Fredholm integral operators.     

Preparation and properties of secondary amides of 1,1-dinitroalkanecarboxylic acids

The previously unknown secondary amides of 1,1-dinitroalkanecarboxylic acids were prepared by the reaction of polynitroimidoyl fluorides with water in the presence of mineral acids. They are inert with respect to electrophiles, but react with nucleophiles with the cleavage of the C-C bond between the carbonyl C atom and the C atom of the dinitromethylene group. An X-ray structural study of the amides was carried out and their thermochemical characteristics were determined.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 877–881, May, 1994.     

New N-nitrosoamines. 2. Transformations of tetrahydro-1,3-oxazines into nitrates of N-nitrosoamino alcohols

The reactions of HNO₃ with tetrahydro-1,3-oxazines 1a—c produced by aminomethylation of diketopiperazine, isatin, and succinimide, respectively, afforded nitrates of amino alcohols [RCH₂NH₂(CH₂)₃ONO₂]⁺NO₃ ^– (4a—c) whose subsequent N-nitrosation (NaNO₂, AcOH) gave nitrates of N-nitrosoamino alcohols RCH₂N(NO)(CH₂)₃ONO₂ (5a—c). The structures of compound 5b,c were established by X-ray diffraction analysis.