Poor Man’s Understanding of Kinks Originating from Strong Electronic Correlations

By means of dynamical mean field theory calculations, it was recently discovered that kinks generically arise in strongly correlated systems, even in the absence of external bosonic degrees of freedoms such as phonons. However, the physical mechanism behind these kinks remained unclear. On the basis of the perturbative and numerical renormalization group theory, we herewith identify these kinks as the effective Kondo energy scale of the interacting lattice system which is shown to be smaller than the width of the central peak.

Figure 1

Comparison of the usual Anderson impurity model of a strongly interacting site coupled via $V$ to an uncorrelated featureless and wide conduction-electron band (left-hand side) and the Hubbard model situation (right-hand side). In the latter case, an electron leaving a correlated site moves within the strongly correlated and narrow band of the central peak. In this situation there is a kink at the effective Kondo energy scale which is smaller than the width of the narrow band.

Figure 2

DMFT(NRG) results for the Hubbard model at $U=2D$. Upper panels: Imaginary (left) and real parts (right) of the self-energy. The latter shows a kink at ${\omega }^{*}$; the linear slopes before and after ${\omega }^{*}$ (straight lines) define a Fermi liquid ($Z_{\mathrm{FL}}$) and central peak renormalization factor ($Z_{CP}$), respectively, whose values are indicated in the other panels. Lower left panel: Spectral function $A(\omega )$. Lower right panel: Spin-spin correlation function with a maximum at ${\omega }^{*}$.

Figure 3

DMFT(NRG) energy levels vs NRG iteration for the Hubbard model at $U=2D$ (left panel) and $U=2.8D$ (right panel). The quantum numbers in brackets indicate the difference in charge ($N$) and the spin-$S_z$ component compared to the lowest energy level whose energy we fixed to zero. The kink energy ${\omega }^{*}$ corresponds to the NRG iterations highlighted in yellow or gray-shaded. The NRG energy levels indicate the crossover to the strong coupling fix point at ${\omega }^{*}$.