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arXiv:cond-mat/0503764 · Physical Review B

Orbital-selective Mott transition in multiband systems: Slave-spin representation and dynamical mean-field theory

Luca de’ Medici, Antoine Georges, Silke Biermann

Published Nov 22, 2005• 242 citations
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Abstract

We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling $J$ when the bandwidth ratio is small and only beyond a critical value of $J$ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at $J=0$ is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization $V$ and replaced at small $V$ by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.

DOI
10.1103/physrevb.72.205124

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We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling JJJ when the bandwidth ratio is small and only beyond a critical value of JJJ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J=0J=0J=0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization VVV and replaced at small VVV by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.
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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 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)t_{12})t12​), where the orbital selective Mott phases (OSMP) show different evolution trends. We find that the negative interorbital hopping (t12<0t_{12}<0t12​<0) can enhance the OSMP regime upon tuning the effective bandwidth ratio. On the contrary, for the cases with positive interorbital hopping (t12>0t_{12}>0t12​>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 t12t_{12}t12​. Our results are also applicable to the hole-overdoped Ba2_22​CuO4−δ_{4-δ}4−δ​ superconductor, which is an orbital-selective Mott compound at half-filling.
We reformulate the time-dependent Gutzwiller approximation by M. Schir\'o and M. Fabrizio, [Phys. Rev. Lett. 105, 076401 (2010)] in the framework of slave-boson mean-field theory, which is used to investigate the dynamical Mott transition of the generic two-band Hubbard model at half filling upon an interaction quench. Interorbital fluctuations lead to notable changes with respect to the single-band case. The singular dynamical transition is replaced by a broad regime of long-lived fluctuations between metallic and insulating states, accompanied by intriguing precursor behavior. A mapping to a spin model proves helpful to analyze the different regions in terms of the evolution of an Ising-like order parameter. Contrary to the static case, singlet occupations remain vital in the Mott-insulating regime with finite Hund's exchange.