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 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 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.
We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising-type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.
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.
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.
Using the dynamical mean field theory with Lanczos method as its impurity solver, we study the orbital-selective Mott transition (OSMT) in the two-orbital J model and Jz model. In the multi-orbital systems, the Mott metal-insulator transition occurs successively when the widths of the bands are different. As the narrow orbital becomes Mott insulator while the wide orbital is still in metallic phase, we find an orbital-selective Mott phase (OSMP). There are two different Hubbard models that are frequently used to describe the OSMT, which are named J model and Jz model, respectively. The J Model is composed of the whole Hund's rule coupling terms, including the spin-flip term, the pair-hopping term and the Ising type Hund's rule coupling term. However, there is only Ising type Hund's rule coupling term in the Jz model.#br#We study the ratio of bandwidth W2/W1 on the OSMT by analyzing the results of the density of states and quasi-particle weight. Comparing the phase diagrams obtained from the J and Jz models with the Hund's rule coupling J(Jz)=U/4, we find that the OSMP region of the J model is much larger than that of the Jz model when W2/W1=0.5 or W2/W1=0.2. When the ratio of bandwidth increases to W2/W1=0.8, the OSMP disappears completely in the Jz model. However in the J model, we can still find the OSMT but the area of the OSMP shrinks significantly. Therefore, the OSMT happens more easily in the J model than in the Jz model.#br#In order to discuss the cooperative effect of the bandwidth and Hund's rule coupling on the OSMT, we compare the phase diagrams for different Hund's rule couplings J(Jz)=U/4 and J(Jz)=U/2. We find that when the bandwidth W2/W1≥q 0.7, the OSMT disappears in Jz model in the case of either Jz=U/4 or Jz=U/2. However, the OSMP always exists in the J model if the bandwidths of the two orbitals are different, suggesting that the rotation invariances of the Hund's rule couplings can protect the OSMP. Therefore, one should be more careful when using the Jz model instead of the J model to study the OSMP.
We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.