We study the effects of interorbital hopping on orbital fluctuations and Mott-Hubbard metal-insulator transition (MIT) in the two-orbital Hubbard model within the extended linearized dynamical mean-field theory. By mapping the model onto an effective model with different bandwidths through the canonical transformation, we find that at half-filling, the increases of the interorbital Coulomb interaction ${U}^{\ensuremath{'}}$ and the Hund's coupling
J drive the MIT, and the critical
Jc for MIT increases with the lift of the interorbital hopping integral
tab. Meanwhile at quarter filling and in the strong correlation regime, the system without
tab exhibits MIT with the decreasing of
J, and favors the orbital liquid ground state. However, the system transits from metal to insulator with the increasing of
tab, accompanied with the rising of the orbital order parameter. These results show the important role of the interorbital hopping in the orbital fluctuation and orbital ordering.
We investigate the quasiparticle dynamics in the two-orbital Hubbard model on the square lattice at quarter filling by means of the cellular dynamical mean-field theory. We show that the Fermi-liquid state is stabilized up to the large Hubbard interactions in the symmetric case without Hund's coupling, and find the heavy quasiparticles around the metal-insulator boundary. It is elucidated that Hund's coupling enhances the antiferro-orbital correlations, which give rise to the pseudogap behavior in the single-particle excitations. We also find the nonmonotonic temperature dependence in the quasiparticle dynamics for intermediate strength of Hund's coupling, and clarify that it is caused by the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations.
We investigate the single-particle dynamics and magnetic properties in the two-orbital Hubbard model on the square lattice at quarter filling by using a cluster extension of dynamical mean field theory. We find that the Fermi-liquid state is stabilized up to the large intra- and inter-orbital interactions in the symmetric case without Hund's coupling. It is clarified that the Hund's coupling enhances the antiferro-orbital fluctuations, which gives rise to the pseudo gap behavior in the single-particle excitations. We also find that the Hund's coupling with intermediate strength causes the competition between the Fermi-liquid formation and the antiferro-orbital fluctuations, resulting in the nonmonotonous temperature dependence in the single-particle dynamics.
We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.
We study a two-orbital attractive Hubbard model with a repulsive Hund's exchange coupling
J as an idealized model for a two-band superconductor. This framework is motivated by a system where a large isotropic electron-phonon coupling drives the on-site Hubbard repulsion
U negative, while leaving the exchange term unaffected. We focus on the intra-orbital (intra-band) singlet superconducting phase and we solve the model at zero temperature and half-filling using Dynamical Mean-Field Theory. Already at
J=0, the two-orbital model features a superconductor-insulator transition as
∣U∣ grows, as opposed to the single-orbital case which remains superconducting for any
U<0. We find that a finite
J strengthens the effect of the attractive
U, both in the normal state and, more significantly, in the superconducting state. However, this pushes the system towards an effectively stronger coupling, hence to a faster transition to the insulating state. Remarkably, the transition from a superconductor to an insulator occurs with a vanishing quasi-particle weight
Z and in a scenario that recalls strongly correlated superconductivity close to a Mott transition, even though the present model is dominated by attractive interactions.