MULTIQUANTA STATES DERIVED FROM DAVYDOVS D(1) ANSATZ .1. EQUATIONS OFMOTION FOR THE SU-SCHRIEFFER-HEEGER HAMILTONIAN

We present equations of motion for the Su-Schrieffer-Heeger (SSH) Hami ltonian derived with the help of ansatz states similar to Davydov's so -called \D1] state for soliton dynamics in proteins. Such an ansatz st ate allows for quantum effects in the lattice and goes beyond previous calculations which mostly apply adiabatic models. In the most general case, called \PHI0], which is treated here in detail, we assume that the coherent-state amplitudes for the lattice depend on the site and t he molecular orbital of the electrons. The equations of motion are der ived from the Lagrangian of the system, a method which is equivalent t o the time-dependent variational principle. In the resulting equations we find that, although the SSH Hamiltonian is a one-particle operator , indirect electron-electron interactions are present in the system wh ich originate from the electron-phonon interactions. Inclusion of dire ct electron-electron interactions, as described in section 8, will giv e insight into the interplay between electron-electron and electron-ph onon interactions which can lead effectively to an attractive force be tween the electrons in systems other than polyacetylene, where bipolar ons are known to be unstable. Further with our time-dependent wavefunc tion also vibrational details of absorption spectra can be computed. F rom the equations of motion several approximations can be derived. In a further approximation, \PHI2], the dependence of the coherent-state amplitudes on the lattice site is neglected. This \PHI2] ansatz state consists of a simple product of the electronic and the lattice wavefun ctions; however, the electrons are not constrained to follow the latti ce dynamics instantaneously as in the adiabatic case. Finally the clas sical adiabatic case is discussed on which soliton-dynamics simulation s are usually based. Further we discuss how to include temperature eff ects in our model. Applications to soliton dynamics are discussed for the example of the \PHI2] model with emphasis on the dependence of the results on soliton width and temperature. We found that in contrast t o results reported in the literature, where a similar ansatz is used, but only one electron is treated explicitly, the solitons remain stabl e also for small soliton widths. This indicates that the interactions of the electrons not occupying the soliton level with the lattice have a stabilizing effect on the soliton. Further our results indicate tha t the temperature model using random forces and dissipation terms to i ntroduce temperature effects has to be applied with extreme care in th is case due to the strong electron-lattice interactions.