A new scheme to calculate dipole-allowed singlets in conjugated polymers.

Properly combined with the Lanczos iteration algorithm, the density matrix renormalization group enables us to directly calculate the dipole-allowed singlet states and the transition moment elements between these states and the ground state for longer chains. Our new scheme does not resort to reflection symmetry and electron-hole symmetry, nor to the construction of different superblocks for the ground state and these singlets separately. As an example, we calculate the ground state and first-excited state in the extended Hubbard model. Our calculations show that for a large U, the transition matrix elements decrease with the chain length; for V around U/2, the transition matrix elements can increase with the chain length, which is consistent with recent experimental results.