The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain.

The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A,B. A density matrix ρ is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of ρ are neglected. It is conjectured that the decreasing behavior of the eigenvalues is Gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH)N up to N=34. A Hilbert space of dimension 5.×1018 is explored. The ground state energy is 10−3 eV within the full CI value in the case N=18. The DMRG method compares favorably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a compar...