Nonlocal correlations induced by Hund's coupling: A cluster DMFT study

We study spatial correlation effects in multiorbital systems, especially in a paramagnetic metallic state subject to Hund's coupling. We apply a cluster extension of the dynamical mean-field theory (DMFT) to the three-orbital Hubbard model away from half filling, where previous single-site DMFT studies revealed that local correlation effects caused by Hund's coupling bring about unusual strongly correlated metallic behaviors. We find that Hund's coupling significantly affects the nonlocal correlations too; it strongly modulates the electron distribution in the momentum space so as to make a momentum region almost half filled and hence strongly correlated. It leads to an anomalous electronic state distinct both from the Fermi liquid and the Mott insulator. We identify the mechanism of the anomalous state with the intersite ferromagnetic correlations induced by Hund's coupling.

Figure 1

(a) Momentum patches used in the present DCA calculation. We call the inner [outer] patch the $(0,0) \left[\right(\pi ,\pi \left)\right]$ patch. The red curve indicates the Fermi surface in the noninteracting case. (b) The noninteracting density of states for each patch. The Fermi level at $U=0$ is shown by a red line. (c) [(d)] The DCA results of the fillings in the $(0,0)$ and $(\pi ,\pi )$ patches for $J=U/4$ with [without] the spin-flip and pair-hopping terms. (e) The result for $J=0$.

Figure 2

(a),(b) Green's functions at the imaginary time $\tau =\beta /2, G_{\mathbf{K}}(\beta /2)$, and (c),(d) the imaginary parts of the self-energies, $\mathrm{Im}{\mathrm{\Sigma }}_{\mathbf{K}}\left(i{\omega }_0\right)$, at the first Matsubara frequency ${\omega }_0=\pi T$, for $(0,0)$ and $(\pi ,\pi )$ patches. Panels (a) and (c) [(b) and (d)] show the results for $J=U/4 [J=0]$.

Figure 3

(a) The on-site spin-spin correlation function $\langle {\widehat{S}}_i^z\left(\tau \right){\widehat{S}}_i^z\left(0\right)\rangle$ and orbital-orbital correlation function $\langle {\widehat{n}}_{li}\left(\tau \right){\widehat{n}}_{mi}\left(0\right)\rangle$ for $J=U/4$. The spin-spin and orbital-orbital correlation functions take positive and negative values, respectively. (b),(c) The intersite spin-spin correlation function $\langle {\widehat{S}}_i^z{\widehat{S}}_j^z\rangle$, intraorbital density-density correlation function $\langle {\widehat{n}}_{li}{\widehat{n}}_{lj}\rangle /4$, and interorbital density-density correlation function $\langle {\widehat{n}}_{li}{\widehat{n}}_{mj}\rangle /4$ for $J=U/4$ and $J=0$, respectively.

Figure 4

The momentum-space configurations of four electrons in the two-site cluster with three orbitals at each site. The up and down arrows indicate the up- and down-spin electrons, respectively. See the main text for more details.