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

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.

Automated summary

The self-trapping transition is investigated in the two-dimensional extended Holstein-Hubbard model, considering both adiabatic and anti-adiabatic cases. A highly accurate phonon state is used as the averaging state to derive an effective electronic Hamiltonian. The system is then solved for weak correlation using the Hartree-Fock mean-field approximation, and for strong correlation, the electronic Hamiltonian is mapped onto an effective t - J model and solved using the Gutzwiller approximation and Zubarev Green's function technique. The self-trapping transition is found to be continuous in the anti-adiabatic regime and discontinuous in the adiabatic regime, across the entire range of Coulomb interaction.