Valence Bond Mapping of Antiferromagnetic Spin Chains

Boson mapping techniques are developed to describe valence bond correlations in quantum spin chains. Applying the method to the alternating bond hamiltonian for a generic spin chain, we derive an analytic expression for the transition points which gives perfect agreement with existing Density Matrix Renormalization Group (DMRG) and Quantum Monte Carlo (QMC) calculations.Comment: 10 pages, Revte

The Density Matrix Renormalization Group for finite Fermi systems

The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the iterative inclusion of sites on a real-space lattice. Based on its enormous success in that domain, it was subsequently proposed that the DMRG could be modified for use on finite Fermi systems, through the replacement of real-space lattice sites by an appropriately ordered set of single-particle levels. Since then, there has been an enormous amount of work on the subject, ranging from efforts to clarify the optimal means of implementing the algorithm to extensive applications in a variety of fields. In this article, we review these recent developments. Following a description of the real-space DMRG method, we discuss the key steps that were undertaken to modify it for use on finite Fermi systems and then describe its applications to Quantum Chemistry, ultrasmall superconducting grains, finite nuclei and two-dimensional electron systems. We also describe a recent development which permits symmetries to be taken into account consistently throughout the DMRG algorithm. We close with an outlook for future applications of the method.Comment: 48 pages, 17 figures Corrections made to equation 19 and table

Double beta decay and theory of nuclear structure

The successes and difficulties of the QRPA are discussed first. In particular, the sensitivity of the double beta decay matrix elements on the choice of the proper nucleon-nucleon interaction and the corresponding set of single particle energies is described. The generalized seniority shell model is discussed. It is shown that it leads to results similar to the results of QRPA, avoiding, however, some of its problem. The problem of the isospin nonconservation and spurious center-of-mass motion is briefly described