Reversal of particle-hole scattering-rate asymmetry in Anderson impurity model

We study the particle-hole asymmetry of the scattering rate in strongly correlated electron systems by examining the cubic ${\omega }^3$ and $\omega T^2$ terms in the imaginary part of the self-energy of the Anderson impurity model. We show that the sign is opposite in the weak-coupling and strong-coupling limits, explaining the differences found in theoretical approaches taking the respective limits as the starting points. The sign change in fact precisely delineates the cross-over between the weak and strong correlation regimes of the model. For weak interaction $U$ the sign reversal occurs for small values of the doping $\delta =1-n$, while for interaction of order $U \approx 2 \Gamma$,$\Gamma$ being the hybridization strength, the cross-over curve rapidly shifts to the large-doping range. This curve based on the impurity dynamics is genuinely different from other cross-over curves defined through impurity thermodynamic and static properties.