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Doctoral thesis In September 2004, I finished my doctoral thesis under the supervision of Prof. Wolfgang von der Linden, at the Institute for Theoretical Physics at TU Graz. The title is: Numerical investigation of strongly correlated electron-phonon models Two years of my work have been supported by DOC [Doctoral Scholarship Program of the Austrian Academy of Sciences]. Abstract
Strongly correlated electron-phonon models with dispersionless phonons and a coupling term of the Holstein type are studied using quantum Monte Carlo (QMC), cluster perturbation theory (CPT), exact diagonalization (ED) and variational approaches. The emphasis lies on the adiabatic regime, which represents a serious challenge and cannot be accurately described analytically at intermediate or strong electron-phonon coupling. The calculations focus on spectral properties, which contain a wealth of information about the excitations of the systems. The small-polaron cross over in the Holstein model with one electron is investigated in one to three dimensions at zero and finite temperature. Using CPT together with the Lanczos method, the one-electron spectral function is obtained at continuous wavevectors. A novel QMC method is developed based on the canonical Lang-Firsov transformation. It is free of any autocorrelations and employs an exact sampling of the phonon degrees of freedom. Consequently, it can be used to study any phonon frequency and electron-phonon coupling strength. It is found that the physics of the Holstein polaron can be described by a simple variational approach, based on an extended Lang-Firsov transformation, which is shown to yield surprisingly good results in parameter regimes where the standard strong-coupling approach fails completely.
Furthermore, the one-electron spectrum of the Holstein-Hubbard model with two electrons is studied by means of CPT. It reveals the competition between polaron and bipolaron states as the electron-phonon coupling and the Coulomb interaction are varied. The dispersion of the bipolaron band is found to display significant deviations from a simple tight-binding band, which may be attributed to next-nearest-neighbor hopping processes. The one-electron QMC algorithm is extended to study the Holstein-Hubbard bipolaron in the adiabatic regime. Investigating the evolution of bipolaron states with increasing temperature, a thermal dissociation of the intersite bipolaron is found at high temperatures, as predicted for the paramagnetic state of some manganites. A variational approach is presented which reproduces qualitatively the effect of retardation on bipolaron formation. Finally, the spinless Holstein model with many electrons is studied in one and two dimensions using CPT in combination with the exact atomic-limit Green function, QMC and the kernel polynomial method. The combination of an improved determinant QMC method and ED calculations on shared-memory systems produces accurate results in the adiabatic regime over the whole range of electron-phonon coupling. Most importantly, starting from the low-density limit, we observe a cross over from a polaronic state to a metallic state with increasing band filling in the intermediate coupling regime. Similar effects are expected to play an important role in materials with strong electron-phonon interaction and high carrier density such as, e.g., the manganites. |