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

TL;DR

This paper investigates how the particle-hole asymmetry in the scattering rate of the Anderson impurity model reverses sign between weak and strong coupling regimes, revealing a crossover that depends on interaction strength and doping.

Contribution

It demonstrates that the sign reversal of the scattering rate asymmetry marks the crossover between weak and strong correlation regimes in the Anderson impurity model, based on impurity dynamics.

Findings

Sign of the scattering rate asymmetry reverses between weak and strong coupling.

Crossover depends on interaction strength and doping levels.

Impurity dynamics-based crossover differs from thermodynamic-based curves.

Abstract

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.