Abstract
An extended Holstein-Hubbard model is studied in two dimensions analytically for both weak and strong correlations. A series of unitary transformations followed by an averaging with a fully-generalized phonon state is performed to obtain an effective electronic Hamiltonian. For weak correlation, the Hartree-Fock approximation is employed and for strong correlation, the electronic Hamiltonian is mapped on to an effective t−J model which is solved using the Gutzwiller approximation and the Zubarev technique. The variation of the effective Coulomb interaction strength is studied for different electron-electron and electron-phonon interaction coefficients and the SDW-CDW phase diagram is plotted using the Mott-Hubbard metallicity criteria. A metallic regime is shown to exist at the SDW-CDW cross-over region and the width of the metallic phase is found to be broader than the result obtained by numerical diagonalization method. The metallic phase is also found to be wider in two dimensions than in one dimension.
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