Failure of Fermi-Liquid Theory at Strong Coupling

TL;DR

This paper examines how strong electron-electron interactions disrupt Fermi-liquid behavior in lattice electrons, revealing the breakdown of Fermi-liquid theory at strong coupling through analytical and self-consistent methods.

Contribution

It provides an analytical solution showing Fermi-liquid properties at weak coupling and demonstrates the failure of Fermi-liquid theory at strong coupling in the Anderson (Hubbard) model.

Findings

Fermi-liquid behavior exists at weak coupling.

Fermi-liquid theory fails at strong coupling.

Critical region influences electron correlation dynamics.

Abstract

We investigate quantitatively the effects of strong electron-electron coupling onto the dynamics of lattice electrons. To that purpose the self-consistent version of the bubble-chain approximation at zero temperature and half filling of the Anderson (Hubbard) model is used. Special attention is paid to a critical region of an electron-hole correlation function shaping the transition from weak to strong interaction. We find an analytic solution with Fermi-liquid properties on the weak-coupling side of the critical region around the two-particle pole. It is shown that Fermi-liquid theory does not lead to a consistent behavior of the self-consistent solution on the strong-coupling side of the critical region.