8,083 research outputs found
The Renormalization Group Method and Quantum Groups: the postman always rings twice
We review some of our recent results concerning the relationship between the
Real-Space Renormalization Group method and Quantum Groups. We show this
relation by applying real-space RG methods to study two quantum group invariant
Hamiltonians, that of the XXZ model and the Ising model in a transverse field
(ITF) defined in an open chain with appropriate boundary terms. The quantum
group symmetry is preserved under the RG transformation except for the
appearence of a quantum group anomalous term which vanishes in the classical
case. This is called {\em the quantum group anomaly}. We derive the new qRG
equations for the XXZ model and show that the RG-flow diagram obtained in this
fashion exhibits the correct line of critical points that the exact model has.
In the ITF model the qRG-flow equations coincide with the tensor product
decomposition of cyclic irreps of with .Comment: LATEX file, 21 pages, no figures. To appear in "From Field Theory to
Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his
60th birthda
Analytic Formulations of the Density Matrix Renormalization Group
We present two new analytic formulations of the Density Matrix
Renormalization Group Method. In these formulations we combine the block
renormalization group (BRG) procedure with Variational and Fokker-Planck
methods. The BRG method is used to reduce the lattice size while the latter are
used to construct approximate target states to compute the block density
matrix. We apply our DMRG methods to the Ising Model in a transverse field (ITF
model) and compute several of its critical properties which are then compared
with the old BRG results.Comment: LATEX file, 25 pages, 8 figures available upon reques
Reusable Knowledge-based Components for Building Software Applications: A Knowledge Modelling Approach
In computer science, different types of reusable components for building software applications were proposed as a direct consequence of the emergence of new software programming paradigms. The success of these components for building applications depends on factors such as the flexibility in their combination or the facility for their selection in centralised or distributed environments such as internet. In this article, we propose a general type of reusable component, called primitive of representation, inspired by a knowledge-based approach that can promote reusability. The proposal can be understood as a generalisation of existing partial solutions that is applicable to both software and knowledge engineering for the development of hybrid applications that integrate conventional and knowledge based techniques. The article presents the structure and use of the component and describes our recent experience in the development of real-world applications based on this approach
The dimer-RVB State of the Four-Leg Heisenberg Ladder: Interference among Resonances
We study the ground state of the 4-leg spin ladder using a dimer-RVB ansatz
and the Lanczos method. Besides the well known resonance mechanism between
valence bond configurations we find novel interference effects among nearby
resonances.Comment: 4 pages, RevTex, 7 eps fig
- …