Effective-field approximations, including DMRG method, for classical inhomogeneous 2D spin lattice models

Abstract

A new approach to derivation of various effective-field approximation for lattice spin models is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous solutions of 2D classical lattice problems. A method, closely related the DMRG method but without necessity to perform any renormalization, is derived, yielding results practically not different from the DMRG ones. The matrix-product wave function of Rommer and \"Ostlund can be constructed from the output of the method. The computational costs of all the derived methods are smaller than those of the DMRG. Most of the results are applicable to the 1D quantum systems, as well.