The conventional, single band Hubbard model captures the dynamics that arise in strongly correlated electron systems in the competition between electron transport and local Coulomb interactions. However, some of the important physics of real lattices is overlooked by its simplicity. The dynamic Hubbard model (DHM) provides additional degrees of freedom for electron states in a lattice by including a higher energy orbital and hybridization parameters for electrons to take advantage of a reduced Coulomb repulsion in the upper orbital when the lattice is at half-filling. This ``relaxation'' of the electronic state is accompanied by an asymmetry between electron and hole quasiparticles in the model. In this thesis we employ the computational tool of multiorbital dynamical mean field theory (MODMFT) to study electron-hole asymmetry in the DHM as evidenced in the behaviour of the quasiparticle weight and optical conductivity of electrons. In agreement with previous exact diagonalization work on the DHM, we find that the relaxation of electronic states is associated with quasiparticle dressing in the hole regime of the lower orbital, and a transfer of optical conductivity spectral weight from low to high frequencies. These observations are evidences of the electron-hole asymmetry in the two-orbital system. In this context, we evaluate the role of two critical variables in the DHM: the local and nonlocal hybridizations which parameterize interorbital electron transitions in the Hamiltonian. We demonstrate that the electron-hole asymmetry of the model has a more complex relationship to these hybridization parameters than previously identified. Mott physics plays an essential role in the quasiparticle dressing due to the local hybridization, while the nonlocal hybridization promotes electron-hole asymmetry by providing a separate channel for electron transport which serves to reduce the quasiparticle weight of holes in the lower band. We also briefly examine the phenomenon of orbital selective Mott transitions in the DHM within the parameter regime of electron state relaxation, and evaluate the role played by the hybridization parameters in this context.
The Dynamic Hubbard Model (DHM) has been introduced as a framework for the electron-hole asymmetry observed in materials like high-temperature superconductors. In this study, we aim to understand the intricate dynamics of hole interactions, particularly focusing on the competition between on-site repulsion and hole-lattice coupling. Our results reveal a striking feature-an effective nearest-neighbor attraction between holes, even in the presence of the on-site repulsion typical of Mott insulators. Notably, the on-site repulsion not only coexists but also enhances the nearest-neighbor coupling. Our exploration of the DHM unravels unexpected and significant characteristics, enriching our understanding of hole interactions in correlated electron systems. The model's capacity to capture both on-site repulsion and effective nearest-neighbor attraction offers a valuable perspective.
We calculate the properties of the two-band Hubbard model using the dynamical cluster approximation. The phase diagram resembles the generic phase diagram of the cuprates, showing a strong asymmetry with respect to electron- and hole-doped regimes, in agreement with experiment. Asymmetric features are also seen in one-particle spectral functions and in the charge, spin, and
d-wave pairing-susceptibility functions. We address the possible reduction of the two-band model to a low-energy single-band one, as it was suggested by Zhang and Rice. Comparing the two-band Hubbard model properties with the single-band Hubbard model ones, we have found similar low-energy physics provided that the next-nearest-neighbor hopping term ${t}^{\ensuremath{'}}$ has a significant value $({t}^{\ensuremath{'}}∕t\ensuremath{\approx}0.3)$. The parameter ${t}^{\ensuremath{'}}$ is the main culprit for the electron-hole asymmetry. However, a significant value of ${t}^{\ensuremath{'}}$ cannot be provided in a strict Zhang and Rice [Phys. Rev. B 37, R3759 (1988); 41, 7243 (1990)] picture where the extra holes added into the system bind to the existing Cu holes forming local singlets. We note that by considering approximate singlet states, such as plaquette states, reasonable values of ${t}^{\ensuremath{'}}$, which capture qualitatively the physics of the two-band model, can be obtained. We conclude that a single-band $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}U$ Hubbard model captures the basic physics of the cuprates concerning superconductivity, antiferromagnetism, pseudogap, and electron-hole asymmetry, but is not suitable for a quantitative analysis or to describe physical properties involving energy scales larger than about 0.5 eV.