Emergent Collective Modes and Kinks in Electronic Dispersions

Recently, it was shown that strongly correlated metallic fermionic systems [Nature Phys. 3, 168 (2007)] generically display kinks in the dispersion of single fermions without the coupling to collective modes. Here we provide compelling evidence that the physical origin of these kinks are emerging internal collective modes of the fermionic systems. In the Hubbard model under study these modes are identified to be spin fluctuations, which are the precursors of the spin excitations in the insulating phase. In spite of their damping, the emergent modes give rise to signatures very similar to features of models including coupling to external modes.

Figure 1

Panel (a) illustrates the relation between real and imaginary parts for an analytic ansatz of the real part with a kink: $\mathrm{Re}\Sigma =\frac{-A^2}{2}\frac{(2\omega +|\omega -a|-|\omega +a|)({\omega }^2-b^2)}{A^2+{\omega }^4}$, with $A\approx 0.62177D$, $a=0.15D$, $b=0.7D$; the imaginary part is computed by the Kramers-Kronig relation. Panel (b) shows the real and imaginary parts of $\Sigma (\omega )$ in DMFT at $U=2.0D$.

Figure 2

$-\mathrm{Im}\Sigma (\omega )$ on a larger scale with two Fermi-liquid fits. The shaded region illustrates additional decay indicated by the arrows.

Figure 3

Deconvolved imaginary part of the local spin susceptibility at positive frequencies for various interactions $U$ in the metallic phase.

Figure 4

Kink positions ${\omega }_{\mathrm{kink}}$ as derived from the quasiparticle weight $Z$ via Eq. (1); $Z$ is found from either the propagator $G$ [19] or the self-energy $\Sigma (\omega )$ in $Z=(1-{\partial }_{\omega }\Sigma (0){)}^{-1}$. Most directly, a fit $A\omega +B(|\omega -{\omega }_{\mathrm{kink}}|-|\omega +{\omega }_{\mathrm{kink}}|)$ to $\mathrm{Re}\Sigma (\omega )$ is used for ${\omega }_{\mathrm{kink}}$; ${\omega }_{\mathrm{kink}}$ is compared to the energies where ${\chi }_{\mathrm{spin}}^{>}$ shows a peak at low $|\omega |$.