6,456 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
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
The Matrix Product Approach to Quantum Spin Ladders
We present a manifestly rotational invariant formulation of the matrix
product method valid for spin chains and ladders. We apply it to 2 legged spin
ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by
the exchange coupling constants, which can be ferromagnetic or
antiferromagnetic along the legs and the rungs of the ladder We compute ground
state energy densities, correlation lengths and string order parameters. We
present numerical evidence of the duality properties of the 3 different non
ferromagnetic spin 1/2 ladders. We show that the long range topological order
characteristic of isolated spin 1 chains is broken by the interchain coupling.
The string order correlation function decays exponentially with a finite
correlation length that we compute. A physical picture of the spin 1 ladder is
given in terms of a collection of resonating spin 1 chains. Finally for ladders
with spin equal or greater than 3/2 we define a class of AKLT states whose
matrix product coefficients are given by 9-j symbols.Comment: REVTEX file, 16 pages, 12 figures, 6 Table
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