Non-Fermi-Liquid Behavior and Double-Exchange Physics in Orbital-Selective Mott Systems

We study a multiband Hubbard model in its orbital-selective Mott phase, in which localized electrons in a narrow band coexist with itinerant electrons in a wide band. The low-energy physics of this phase is shown to be given by a generalized double-exchange model. The high-temperature disordered phase thus differs from a Fermi liquid, and displays a finite scattering rate of the conduction electrons at the Fermi level, which depends continuously on the spin anisotropy.

Figure 1

Broad band self-energy $\mathrm{Im}{\Sigma }_c(i{\omega }_n)$ for different temperatures ($\beta D_c=40$, 60, 80, and 120 correspond to circles, empty and filled squares, and diamonds, respectively). In the $J=0$ case (black online) $\mathrm{Im}{\Sigma }_c(i\omega )$ extrapolates linearly to zero (Fermi-liquid behavior), whereas for $J=0.2$ (red online, bottom curve of main figure) a finite lifetime is found. Inset: $\mathrm{Im}{G}_d(i{\omega }_n)$ and $\mathrm{Im}{G}_c(i{\omega }_n)$ for $U=0.8{\mathrm{D}}_c$ and $J=0.2D_c$. QMC results (symbols) correspond to finite temperatures ($\beta D_c=40,60,80,120$ given by circles, squares, triangles up and down, respectively), while the ED data (lines) are at zero temperature.

Figure 2

Spectral functions for $J=0$ and $J=0.2$ ($U=0.8D_c,\beta D_c=120$) calculated from QMC data. The narrow band ${\rho }_d(\omega )$ (dashed line) displays a gap or pseudogap in both cases. For $J=0$, ${\rho }_c(\omega )$ (solid line) coincides at $\omega =0$ with the noninteracting density of states (dashed-dotted line), as a consequence of Luttinger theorem, while this condition is clearly violated at $J\ne 0$ [${\rho }_c(0)<{\rho }_{0c}(0)$].

Figure 3

Green’s function in imaginary time for $U=0.8D_c$, $J=0.2D_c$, $\beta =80$, computed from QMC data. The full triangles and squares (red curves online) give the results for the two-band model; the effective one-band model Green’s function (empty black circles) fit the wide band of the two-band model perfectly. The solid lines (green curves online) represent the auxiliary Green’s functions of the $S_z=\pm 1/2$ sectors of the effective 1-band model.

Figure 4

Low-energy part of $\mathrm{Im}{\Sigma }_c(i\omega )$, obtained by ED at $T=0$ for $U=1.2D_c,J=0.15U$, and different values of $\alpha$ (0, 0.3, 0.5, 0.7, and 1 from bottom to top). It extrapolates to zero at $\omega =0$ only in the case of fully symmetric interactions ($\alpha =1$, solid curve, red online). Inset: Zero-frequency extrapolation of the Green’s function as a function of $J$ and for different values of $\alpha =1$, 0.7, 0.5, and 0 (from bottom to top). In the case of a fully $SU(2)$ symmetric interaction vertex ($\alpha =1$) the Luttinger pinning condition $\mathrm{Im}G(0)=-2/D_c$ is fulfilled. As soon as this symmetry is broken ($\alpha <1$), the pinning condition is lost.

Figure 5

Low-energy behavior of $\mathrm{Im}{\Sigma }_c(i\omega )$ obtained by ED for $U=1.2D_c$ and $J=0.15U$ (squares) and $J=0.25U$ (circles) in the symmetric case $\alpha =1$. Solid lines are low-frequency fits of the data to the function $F(\omega )=-a/[(\ln \omega {)}^2+b\ln \omega +c]$. Inset: $\mathrm{Im}{\Sigma }_c(i\omega )$ for $U=0.8D_c$, $J=0.2D_c$, $\alpha =0$, computed from QMC data without spin symmetrization. Empty and solid circles, squares and triangles (up and down) correspond to $\beta D_c=10$, 20, 30, 50, and 120. The last two temperatures correspond to a ferromagnetic state.