Application of the Dyson-type boson mapping for low-lying electron excited states in molecules

ken mcphail, diane walters;

In many-electron systems, particularly when it is the case that the system consists of quasiparticles having almost no interaction with each other, the approaches to considering a quasiparticle to be a basic particle are important. We propose a bosonization method of the system in which a quasi-particle consists of electron–hole pairs. Low-lying electron excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi-particles consists of the electron–hole pairs.We consider the fundamental model Hamiltonian, and transformthis into the quasi-particle representation Hamiltonian. Then, we transform these quasi-particles into bosons
by using the Dyson-type boson mapping method. The obtained Dyson-type boson Hamiltonian enables a straightforward interpretation of the low-lying electron excited states and facilitates
their calculation. To confirm the usefulness of this method, we apply this to the π-electrons system of the ethylene molecule.