Renormalization-group studies of the Hubbard-Peierls Hamiltonian for finite polyenes

Abstract

We have applied a numerical renormalization-group technique to study the Hubbard-Peierls model for (CH${)}_{\mathrm{x}}$. The method provides accurate many-body wave functions and energies for the ground and low-lying excited states of finite polyenes. We report tests of the method for finite chains (N=16) which show that the technique accurately reproduces known results in the noninteracting particle limit (U=0) and in the highly correlated limit (U/4t≫1) and agrees well with Monte Carlo data where available for intermediate U. The model is applied to study correlation effects on the ground-state dimerization amplitude and to the ordering of the low-lying excited states of the rigid-lattice spectrum. Extension of the method to even longer systems appears to be quite practical.