Distinct nature of orbital-selective Mott phases dominated by low-energy local spin fluctuations

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.

Figure 1

Entanglement entropy as a function of $U$ for three different bandwidth ratio in the case of full (a) and Ising (b) Hund's coupling. Dashed lines indicate the phase boundaries.

Figure 2

Orbital resolved densities of states in metallic states (a), (b), orbital-selective Mott phases (c), (d), and Mott insulating states (e), (f) for full and Ising Hund's coupling cases. Here, a Lorentz broadening factor of 0.1 is used.

Figure 3

Orbital resolved imaginary parts of self-energies in metallic states (a), (b), orbital-selective Mott phases (c), (d), and Mott insulating states (e), (f) for full and Ising Hund's coupling cases.

Figure 4

Total local dynamical spin susceptibilities in metallic and orbital-selective Mott (OSM) phases for full (a) and Ising (b) Hund's coupling cases. Here, a Lorentz broadening factor of 0.1 is used. (c) and (d) show $\langle S_z^2\rangle$ as a function of $U$ for full and Ising Hund's coupling cases, respectively.

Figure 5

The $U$ dependence of DOS in the OSM phase for the cases of full (a) and Ising (b) Hund's coupling. Solid lines denote wide band and dashed lines represent narrow band. Here, a Lorentz broadening factor of 0.1 is used.

Figure 6

The evolution of DOS of wide band at the Fermi level as a function of the lorentz broadening factor $\eta$ in full and Ising Hund's coupling cases. Solid lines with empty circle denote full Hund's coupling; dashed lines with filled diamond denote Ising Hund's coupling.

Figure 7

The $U$ dependence of the imaginary part of self-energy in the Matsubara frequency $\mathrm{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)$ in the OSM phase in the case of full (a) and Ising (b) Hund's coupling. Solid lines denote wide band and dashed lines represent narrow band.

Figure 8

The $U$ dependence of the real part of self-energy in real frequency $\mathrm{Re}\mathrm{\Sigma }\left(\omega \right)$ of wide band from metallic to the OSM phase for full (a) and Ising (b) Hund's coupling. Here, a Lorentz broadening factor of 0.1 is used.

Figure 9

The evolution of dynamical spin susceptibility ${\chi }_{\text{sp}}^{\text{tot}}\left(\omega \right)$ as a function of $U$ in the case of full (a) and Ising (b) Hund's coupling. Here, a Lorentz broadening factor of 0.1 is used.

Figure 10

The orbitally resolved dynamical spin susceptibility ${\chi }_{sp}^{\alpha \beta }\left(\omega \right)$ in the OSM phases for both full (red) and Ising (black) Hund's coupling. Here, a Lorentz broadening factor of 0.1 is used.

Figure 11

The ground-state energy (a) and the first derivative of the ground-state energy (b) with respect to $U$ for full and Ising Hund's coupling as a function of interaction $U$.

Figure 12

Comparison of the entanglement entropies as a function of $U$ for full and Ising Hund's coupling calculated in the framework of DMFT with ED solver where six bath sites and four bath sites coupled to each impurity, namely 12 bath sites and eight bath sites in total, respectively, are taken into account.

Figure 13

The comparison between ${\widehat{g}}_{0\gamma }\left(i{\omega }_n\right)$ and $g_{0\gamma }\left(i{\omega }_n\right)$ calculated by 12 bath sites (six bath sites per impurity) for full Hund's coupling. Solid lines denote $g_{0\gamma }\left(i{\omega }_n\right)$ and dashed lines denote ${\widehat{g}}_{0\gamma }\left(i{\omega }_n\right)$. The dashed and solid lines are completely overlapped, indicating negligible effect of bath discretization.

Figure 14

The comparison between ${\widehat{g}}_{0\gamma }\left(i{\omega }_n\right)$ and $g_{0\gamma }\left(i{\omega }_n\right)$ computed by 12 bath sites, namely six bath sites per impurity, for Ising Hund's coupling. Solid lines denote $g_{0\gamma }\left(i{\omega }_n\right)$ and dashed lines denote ${\widehat{g}}_{0\gamma }\left(i{\omega }_n\right)$. The dashed and solid lines are completely overlapped, indicating negligible effect of bath discretization.

Figure 15

The orbital-resolved density of states in metallic phase (a), (b), the OSM phase (c), (d), and Mott insulating phase (e), (f). Here, a Lorentz broadening factor of 0.1 is used.

Figure 16

The imaginary part of self-energy in Matsubara frequency $\mathrm{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)$ in metallic phase (a), (b), the OSM phase (c), (d), and Mott insulating phase (e), (f).

Figure 17

Dynamical spin susceptibility for full (a) and Ising (b) Hund's coupling, and static spin susceptibility for full (c) and Ising (d) Hund's coupling. In (a) and (b), a Lorentz broadening factor of 0.1 is used.