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arXiv:0910.3911 · Physical Review Letters

Dynamical Cluster Approximation Study of the Anisotropic Two-Orbital Hubbard Model

Hunpyo Lee, Yu‐Zhong Zhang, Harald O. Jeschke, Roser Valentí, H. Monien

Published Jan 15, 2010• 26 citations
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Abstract

We investigate the properties of a two-orbital Hubbard model with unequal bandwidths on the square lattice in the framework of the dynamical cluster approximation (DCA) combined with a continuous-time quantum Monte Carlo algorithm. We explore the effect of short-range spatial fluctuations on the nature of the metal-insulator transition and the possible occurrence of an orbital-selective Mott transition (OSMT) as a function of cluster size N{c}. We observe that for N{c}=2 no OSMT is present, instead a band insulator state for both orbitals is stabilized at low temperatures due to the appearance of an artificial local ordered state. For N{c}=4 the DCA calculations suggest the presence of five different phases which originate out of the cooperation and competition between spatial fluctuations and orbitals of different bandwidths and an OSMT phase is stabilized. Based on our results, we discuss the nature of the gap opening.

DOI
10.1103/physrevlett.104.026402

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We investigate the properties of a two-orbital Hubbard model with unequal bandwidths on the square lattice in the framework of the dynamical cluster approximation (DCA) combined with a continuous-time quantum Monte Carlo algorithm. We explore the effect of short-range spatial fluctuations on the nature of the metal-insulator transition and the possible occurrence of an orbital-selective Mott transition (OSMT) as a function of cluster size N{c}. We observe that for N{c}=2 no OSMT is present, instead a band insulator state for both orbitals is stabilized at low temperatures due to the appearance of an artificial local ordered state. For N{c}=4 the DCA calculations suggest the presence of five different phases which originate out of the cooperation and competition between spatial fluctuations and orbitals of different bandwidths and an OSMT phase is stabilized. Based on our results, we discuss the nature of the gap opening.
We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two-band fermion Hubbard model using determinant quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFMO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that LRAFMO plays a key role in the transitions.
We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
Abstract The anisotropic two‐orbital Hubbard model with different bandwidths and degrees of frustration in each orbital is investigated in the framework of both single‐site dynamical mean‐field theory (DMFT) as well as its cluster extension (DCA) for clusters up to four sites combined with a continuous‐time quantum Monte Carlo algorithm. This model shows a rich phase diagram which includes the appearance of orbital selective phase transitions, non‐Fermi liquid behavior as well as antiferromagnetic metallic states. We discuss the advantages and drawbacks of employing the single‐site DMFT with respect to DCA and the consequences for the physical picture obtained out of these calculations. Finally, we argue that such a minimal model may be of relevance to understand the nature of the antiferromagnetic metallic state in the iron‐pnictide superconductors as well as the origin of the small staggered magnetization observed in these systems.
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.
We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for 1/31/31/3 filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.