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arXiv:cond-mat/0506150 · Physical Review B

Finite-temperature Mott transitions in the multiorbital Hubbard model

Kensuke Inaba, Akihisa Koga, Sei-ichiro Suga, Norio Kawakami

Published Aug 8, 2005• 52 citations
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Abstract

We investigate the Mott transitions in the multiorbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to fourfold degenerate bands. We discuss how the first-order Mott transition points ${U}_{c1}$ and ${U}_{c2}$ as well as the critical temperature ${T}_{c}$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.

DOI
10.1103/physrevb.72.085112

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We investigate the Mott transitions in the multiorbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to fourfold degenerate bands. We discuss how the first-order Mott transition points Uc1{U}_{c1}Uc1​ and Uc2{U}_{c2}Uc2​ as well as the critical temperature Tc{T}_{c}Tc​ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.
Mott transitions in the two-orbital Hubbard model with different bandwidths are investigated at finite temperatures. By means of the self-energy functional approach, we discuss the stability of the intermediate phase with one orbital localized and the other itinerant, which is caused by the orbital-selective Mott transition (OSMT). It is shown that the OSMT realizes two different coexistence regions at finite temperatures in accordance with the recent results of Liebsch. We further find that the particularly interesting behavior emerges around the special condition U=U′U=U'U=U′ and J=0, which includes a new type of the coexistence region with three distinct states. By systematically changing the Hund coupling, we establish the global phase diagram to elucidate the key role played by the Hund coupling on the Mott transitions.
The two-orbital degenerate Hubbard model with distinct hopping integrals is studied by combining dynamical mean-field theory with quantum Monte Carlo simulations. The role of orbital fluctuations for the nature of the Mott transition is elucidated by examining the temperature dependence of spin, charge, and orbital susceptibilities as well as the one-particle spectral function. We also consider the effect of the hybridization between the two orbitals, which is important particularly close to the Mott transition points. The introduction of the hybridization induces orbital fluctuations, resulting in the formation of a Kondo-like heavy-fermion behavior, similarly to fff-electron systems, but involving electrons in bands of comparable width.
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.
Using the quantum Monte Carlo technique we compute thermodynamics and spectra for the orbitally degenerate Hubbard model in infinite spatial dimensions. With increasing orbital degeneracy we find in the one-particle spectra broader Hubbard bands (consistent with increased kinetic energy), a narrowing Mott gap, and increasing quasiparticle spectral weight. Hund's rule exchange coupling decreases the critical on-site Coulomb energy for the Mott transition. The metallic regime resistivity for twofold degeneracy is quadratic in temperature at low temperatures.