Self-trapping transition in a two dimensional extended Holstein-Hubbard model: A mean-field study

Abstract

The self-trapping transition is studied within the framework of the two-dimensional extended Holstein-Hubbard model for both adiabatic and anti-adiabatic cases. A highly accurate phonon state is chosen as the averaging state to obtain an effective electronic Hamiltonian which is solved for the two different Coulomb correlation regimes separately. For weak correlation, the Hartree-Fock mean-field approximation is employed and for strong correlation, the electronic Hamiltonian is mapped on to an effective t−J model which is solved by using the Gutzwiller approximation and the Zubarev Green's function technique. For the entire range of the Coulomb interaction, the self-trapping transition turns out to be continuous for the anti-adiabatic regime and for the adiabatic regime the transition it is found to be discontinuous.