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arXiv:1312.0100

Magnetic instability of the orbital-selective Mott phase

Markus Greger, Michael Sekania, Marcus Kollar

Published Nov 30, 2013• 1 citation
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Abstract

We characterize the low-energy physics of the two-orbital Hubbard model in the orbital-selective Mott phase, in which one band is metallic and the other insulating. Using dynamical mean-field theory with the numerical renormalization group at zero temperature, we show that this phase has a ferromagnetic instability for any nonzero Hund's rule exchange interaction, which can be understood in terms of an effective spin-1 Kondo Hamiltonian. The metallic band therefore behaves as a singular Fermi liquid for which the self-energy has a logarithmic singularity at the Fermi energy.

DOI
10.48550/arxiv.1312.0100

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We characterize the low-energy physics of the two-orbital Hubbard model in the orbital-selective Mott phase, in which one band is metallic and the other insulating. Using dynamical mean-field theory with the numerical renormalization group at zero temperature, we show that this phase has a ferromagnetic instability for any nonzero Hund's rule exchange interaction, which can be understood in terms of an effective spin-1 Kondo Hamiltonian. The metallic band therefore behaves as a singular Fermi liquid for which the self-energy has a logarithmic singularity at the Fermi energy.
We study the finite-temperature properties of the half-filled two-band Hubbard model in the presence of Hund's rule coupling and orbital anisotropy. We use the mean-field treatment of the Z2{Z}_{2}Z2​ slave-spin theory with a finite-temperature extension of the zero-temperature gauge variable previously developed by Hassan and de' Medici [Phys. Rev. B 81, 035106 (2010)]. We consider the instability of the Fermi-liquid phases and how it is enhanced by the Hund's rule. We identify paramagnetic solutions that have zero quasiparticle weight with a bad metal, and the first-order transition temperature between the bad metal and the Fermi-liquid phase as a coherence temperature that signals the crossover to the bad metallic state. When orbital anisotropy is present, we found an intermediate transition to an orbital-selective bad metal (OSBM), where the narrow band becomes a bad metal while the wide band remains a renormalized Fermi liquid. The temperatures Tcoh{T}_{\text{coh}}Tcoh​ and TOSBM{T}_{\text{OSBM}}TOSBM​ at which the system transitions to the bad metal phases can be orders of magnitude less than the Fermi temperature associated with the noninteracting band. The parameter dependence of the temperature at which the OSBM is destroyed can be understood in terms of a ferromagnetic Kondo-Hubbard lattice model. In general, Hund's rule coupling enhances the bad metallic phases, reduces interorbital charge fluctuations, and increases spin fluctuations. The qualitative difference found in the ground state whether the Hund's rule is present or not, related to the degeneracy of the low-energy manifold, is also maintained for finite temperatures.
Recent advances in the field of quantum Monte Carlo simulations for impurity problems allow---within dynamical mean field theory---for a more thorough investigation of the two-band Hubbard model with a narrow-wide band and SU(2)-symmetric Hund's exchange. The nature of this transition has been controversial, and we establish that an orbital-selective Mott-Hubbard transition exists. The wide band still shows metallic behavior after the narrow band became insulating---not a pseudogap as for an Ising Hund's exchange. The coexistence of two solutions with a metallic wide band and an insulating or metallic narrow band indicates, in general, first-order transitions.
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.
Quantum orbital-selective Mott (OSM) transitions are investigated within dynamical mean-field theory based on a two-orbital Hubbard model with different bandwidth at half filling. We find two distinct OSM phases both showing coexistence of itinerant electrons and localized spins, dependent on whether the Hund's coupling is full or of Ising type. The critical values and the nature of the OSM transitions are efficiently determined by entanglement entropy. We reveal that vanishing of the Kondo energy scale evidenced by absence of local spin fluctuations at low frequency in local dynamical spin susceptibility is responsible for the appearance of non-Fermi-liquid OSM phase in Ising Hund's coupling case. We argue that this scenario can also be applied to account for emergent quantum non-Fermi liquid in the one-band Hubbard model when short-range antiferromagnetic order is considered.
We calculate the spectra and spin susceptibilities of a Hubbard model with two bands having different bandwidths but the same on-site interaction, with parameters close to the orbital-selective Mott transition, using dynamical mean-field theory. If the Hund's rule coupling is sufficiently strong, one common energy scale emerges which characterizes both the location of kinks in the self-energy and extrema of the diagonal spin susceptibilities. A physical explanation of this energy scale is derived from a Kondo-type model. We infer that for multiband systems local spin dynamics rather than spectral functions determine the location of kinks in the effective band structure.