THE DENSITY-MATRIX RENORMALIZATION-GROUP METHOD APPLIED TO INTERACTION ROUND A FACE HAMILTONIANS

Given a Hamiltonian with a continuous symmetry one can generally facto rize that symmetry and consider the dynamics on invariant Hilbert spac es. In statistical mechanics this procedure is known as the vertex-IRF map, and in certain cases, like rotational invariant Hamiltonians, it can be implemented via group theoretical techniques. Using this map w e translate the DMRG method, which applies to 1D vertex Hamiltonians, into a formulation adequate to study IRF Hamiltonians. The advantage o f the IRF formulation of the DMRG method (we name it IRF-DMRG), is tha t the dimensions of the Hilbert spaces involved in numerical computati ons are smaller than in the vertex-DMRG, since the degeneracy due to t he symmetry has been eliminated. The IRF-DMRG admits a natural and geo metric formulation in terms of the paths or string algebras used in ex actly Integrable systems and conformal field theory. We illustrate the IRF-DMRG method with the study of the SOS model which corresponds to the spin-1/2 Heisenberg chain and the RSOS models with a Coxeter diagr am of type A, which corresponds to the quantum group invariant XXZ cha in. (C) 1997 Elsevier Science B.V.