A generalized multiorbital Hubbard model, which includes on-site interorbital electron hoppings, is introduced and studied on an arbitrary basis. In a general system the on-site interorbital single-electron hopping may exist realistically between two orbitals, e.g., the excitation of electrons or flow of electrons between two hybridized states, and is hence one of the most basic interactions like the intersite hopping and the on-site Coulomb interactions. It is shown in this work how the higher order interactions can be well incorporated (or generated) in the equations of motion from the basic interactions in the Hamiltonian, which has made it possible and also given a self-consistent way to investigate these higher order correlation effects. The two-orbital Hubbard model is studied numerically in the paramagnetic case to demonstrate the influence of the single-electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site interorbital hopping suppresses the so-called orbital-selective Mott transition.
A generalized multiorbital Hubbard model, which includes on-site interorbital electron hoppings, is introduced and studied on an arbitrary basis. In a general system the on-site interorbital single-electron hopping may exist realistically between two orbitals, e.g., the excitation of electrons or flow of electrons between two hybridized states, and is hence one of the most basic interactions like the intersite hopping and the on-site Coulomb interactions. It is shown in this work how the higher order interactions can be well incorporated (or generated) in the equations of motion from the basic interactions in the Hamiltonian, which has made it possible and also given a self-consistent way to investigate these higher order correlation effects. The two-orbital Hubbard model is studied numerically in the paramagnetic case to demonstrate the influence of the single-electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site interorbital hopping suppresses the so-called orbital-selective Mott transition.
The localization-delocalization transition is at the heart of strong correlation physics. Recently, there is great interest in multiorbital systems where this transition can be restricted to certain orbitals, leading to an orbital-selective Mott phase (OSMP). Theoretically, the OSMP is widely studied for kinetically decoupled orbitals, but the effect of interorbital hopping remains unclear. Here, we show how nonlocal interorbital hopping leads to local hybridization in single-site dynamical mean-field theory (DMFT). Under fairly general circumstances, this implies that, at zero temperature, the OSMP, involving the Mott-insulating state of one orbital, is unstable against interorbital hopping to a different, metallic orbital. We further show that the coherence scale below which all electrons are itinerant is very small and gets exponentially suppressed even if the interorbital hopping is not overly small. Within this framework, the OSMP with interorbital hopping may thus reach down to extremely low temperatures T, but not to T=0. Accordingly, it is part of a coherence-incoherence crossover and not a quantum critical point. We present analytical arguments supported by numerical results using the numerical renormalization group as a DMFT impurity solver. We also compare our findings with previous slave-spin studies.
The influence of short-range Coulomb correlations on the Mott transition in the single-band Hubbard model at half filling is studied within cellular dynamical mean-field theory for square and triangular lattices. Finite-temperature exact diagonalization is used to investigate correlations within two-, three-, and four-site clusters. Transforming the nonlocal self-energy from a site basis to a molecular-orbital basis, we focus on the interorbital charge transfer between these cluster molecular orbitals in the vicinity of the Mott transition. In all cases studied, the charge transfer is found to be small, indicating weak Coulomb-induced orbital polarization despite sizable level splitting between orbitals. These results demonstrate that all cluster molecular orbitals take part in the Mott transition and that the insulating gap opens simultaneously across the entire Fermi surface. Thus, at half filling we do not find orbital-selective Mott transitions or a combination of band filling and Mott transition in different orbitals. Nevertheless, the approach toward the transition differs greatly between cluster orbitals, giving rise to a pronounced momentum variation along the Fermi surface, in agreement with previous works. The near absence of Coulomb-induced orbital polarization in these clusters differs qualitatively from single-site multiorbital studies of several transition-metal oxides, where the Mott phase exhibits nearly complete orbital polarization as a result of a correlation driven enhancement of the crystal-field splitting. The strong single-particle coupling among cluster orbitals in the single-band case is identified as the source of this difference.
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.
The effect of interorbital hopping on the orbital selective Mottness in a two-band correlation system is investigated by using the dynamical mean-field theory with the Lanczos method as impurity solver. We construct the phase diagram of the two-orbital Hubbard model with interorbital hopping (t12), where the orbital selective Mott phases (OSMP) show different evolution trends. We find that the negative interorbital hopping (t12<0) can enhance the OSMP regime upon tuning the effective bandwidth ratio. On the contrary, for the cases with positive interorbital hopping (t12>0), the OSMP region becomes narrow with the increase of orbital hybridization until it disappears. It is also shown that a new OSMP emerges for a large enough positive interorbital hopping, owing to the role exchange of wide and narrow effective orbitals caused by the large t12. Our results are also applicable to the hole-overdoped Ba2CuO4−δ superconductor, which is an orbital-selective Mott compound at half-filling.
The effect of interorbital hopping on orbital selective Mottness in a two-band correlation system is investigated by using the dynamical mean-field theory with the Lanczos method as impurity solver. The phase diagrams of the two-orbital Hubbard model with non-local interorbital hopping (t12) , where the orbital selective Mott phases (OSMP) region is expanded by the increasing of the interorbital hopping. We compare the results obtained by self-consistent relations of Bethe lattice and squate lattice based on DMFT procedure, and the general OSMP physics of Bethe lattice is consistent with that of the square lattice while the critical points of two kinds of lattices are different. We extend the method to the study of half-filled Ba2CuO4–δ materials. By comparing with the band structure obtained from the density functional theory (DFT), it is found that the isotropic inter-orbital hopping has a great influence on the bandstructure. The DFT bandstructure in DMFT is considered, and the phase diagram of the material is obtained. The half-filled Ba2CuO4–δ should be orbital-selective Mott compound according to our results.
The Mott transition in a multiorbital Hubbard model involving subbands of different widths is studied within the dynamical mean-field theory. Using the iterated perturbation theory for the quantum impurity problem it is shown that at low temperatures interorbital Coulomb interactions give rise to a single first-order transition rather than a sequence of orbital selective transitions. Impurity calculations based on the Quantum Monte Carlo method confirm this qualitative behavior. Nevertheless, at finite temperatures, the degree of metallic or insulating behavior of the subbands differs greatly. Thus, on the metallic side of the transition, the narrow band can exhibit quasi-insulating features, whereas on the insulating side the wide band exhibits pronounced bad-metal behavior. This complexity might partly explain contradictory results between several previous works.