1996/10/31 by G. Sierra, Germán Sierra, T. Nishino +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Conformal field theory #Coxeter group #Density matrix renormalization group #Factorization #Hamiltonian (control theory) #Hilbert space #Integrable system #Invariant (physics) #Quantum chaos and dynamical systems #Quantum many-body systems #Renormalization group #Symmetry group #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00217-4
published as Nucl.Phys. B495 (1997) 505 · 22 pages, Latex, 18 figures in Postscript files
arxiv created 1996/10/31 · openalex publication_date 1997/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Given a Hamiltonian with a continuous symmetry one can generally factorize that symmetry and consider the dynamics on invariant Hilbert Spaces. In Statistical Mechanics this procedure is known as the vertex-IRF map, and in certain cases, like rotational invariant Hamiltonians, can be implemented via group theoretical techniques. Using this map we translate the DMRG method, which applies to 1d vertex Hamiltonians, into a formulation adequate to study IRF Hamiltonians. The advantage of the IRF formulation of the DMRG method ( we name it IRF-DMRG), is that the dimensions of the Hilbert Spaces involved in numerical computations are smaller than in the vertex-DMRG, since the degeneracy due to the symmetry has been eliminated. The IRF-DMRG admits a natural and geometric formulation in terms of the paths or string algebras used in Exactly 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 Coxeter diagram of type A, which correspond to the quantum group invariant XXZ chain.