Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains

¹ Instituto de Estructura de la Materia, CSIC - Madrid, Spain
² Departamento de Física Teórica I, Universidad Complutense - Madrid, Spain
³ Department of Physics, Faculty of Science, Kobe University - Japan
⁴ Instituto de Matemáticas y Física Fundamental, CSIC - Madrid, Spain

Received: 7 April 1998
Accepted: 25 June 1998

Abstract

We study the relationship between the Density Matrix Renormalization Group (DMRG) and the variational matrix product method (MPM). In the latter method one can also define a density matrix whose eigenvalues turn out to be numerically close to those of the DMRG. We illustrate our ideas with the spin-1 Heisenberg chain, where we compute the ground-state energy and the spin correlation length. We also give a rotational invariant formulation of the MPM.