An Improved Initialization Procedure for the Density-Matrix Renormalization Group

Abstract

We propose an initialization procedure for the density-matrix renormalization group (DMRG): the recursive sweep method. In a conventional DMRG calculation, the infinite-system algorithm, where two new sites are added to the system at each step, has been used to achieve the target system size. We then need to obtain the ground state for a different system size for every site addition. Thus, 1) it is difficult to supply a good initial vector for the numerical diagonalization for the ground state, and 2) when the system reduced to a 1D one that consists of an array of nonequivalent sites as in the case of ladders or in the Hubbard–Holstein model, special care has to be taken. Our procedure, which we call the recursive sweep method, provides a solution to these problems and in fact provides a faster algorithm for the Hubbard model and the complicated ones such as the Hubbard–Holstein model.