G. Fano et al., THE DENSITY-MATRIX RENORMALIZATION-GROUP METHOD - APPLICATION TO THE PPP MODEL OF A CYCLIC POLYENE CHAIN, The Journal of chemical physics, 108(22), 1998, pp. 9246-9252
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].