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Employing the recently developed self-consistent variational basis generation scheme, we have investigated the bipolaron-bipolaron interaction within the purview of the Holstein-Hubbard and the extended-Holstein-Hubbard (F2H) models on a discrete one-dimensional lattice. The density-matrix renormalization group method has also been used for the Holstein-Hubbard model. We have shown that there exists no bipolaron-bipolaron attraction in the Holstein-Hubbard model. In contrast, we have obtained clear-cut bipolaron-bipolaron attraction in the F2H model. Composite bipolarons are formed above a critical electron-phonon coupling strength, which can survive the finite Hubbard U effect. We have constructed the phase diagram of F2H polarons and bipolarons, and discussed the phase separation in terms of the formation of composite bipolarons. [ABSTRACT FROM AUTHOR]

We have developed a self-consistent scheme of generating variational basis based on the exact diagonalization, which can be applied efficiently to various types of electron-phonon systems. This scheme is quite general and brings down the size of the variational space by an order of magnitude or even more in some cases to reproduce the most precise ground state energies and correlation functions available in the literature. This method has enormous potential for application to systems with more electrons or in higher dimensions, which are still beyond the reach of exact diagonalization just because of the sheer size of their variational space needed to get reasonably convergent results. [ABSTRACT FROM AUTHOR]

We have investigated bipolarem formation in the Holstein-Hubbard and the Fröhlich-Hubbard model on a discrete one-dimensional lattice. Phonon enriched basis has been generated by exploiting the idea of the Lang-Firsov transformation, which results in better convergence in the strong coupling regime. The incorporation of the finite-range electron-phonon (e-ph) interaction reduces the bipolaren effective mass. We systematically increase the spatial extent of the e-ph interaction to study the effect of the long-range tail of the Fröhlich model. The electron-electron (e-e) interaction also plays a crucial role in lowering the effective mass for both the Holstein and the Fröhlich bipolarons. In the presence of the extended e-e interaction, the intersite SI Holstein bipolaren becomes unstable, while the effective mass of the Fröhlich bipolaren becomes significantly reduced for both the spin singlet and triplet cases. [ABSTRACT FROM AUTHOR]