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 W hite for the study of strongly interacting electron systems is reviewe d; the method is variational and considers a system of localized elect rons as the union of two adjacent fragments A,B. A density matrix rho is introduced, whose eigenvectors corresponding to the largest eigenva lues are the most significant, the most probable states of A in the pr esence of B; these states are retained, while states corresponding to small eigenvalues of rho are neglected. It is conjectured that the dec reasing behavior of the eigenvalues is Gaussian. The DMRG method is te sted on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH), u p to N = 34. A Hilbert space of dimension 5. X 10(18) 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 comparison is made wit h the DMRG energy values. Finally, the spin-spin and density-density c orrelation functions are computed; the results suggest that the antife rromagnetic order of the exact solution does not extend up to large di stances but exists locally. No charge density waves are present. (C) 1 998 American Institute of Physics. [S0021-9606(98)00822-8].