Crossover from Fermi to Non-Fermi Liquid in Two-Dimensional Interacting Fermions

TL;DR

This paper investigates the transition from Fermi liquid to non-Fermi liquid behavior in two-dimensional interacting fermions by analyzing self-energy divergences and their dependence on interaction strength and momentum.

Contribution

It provides a third-order perturbative analysis of self-energy in 2D fermions, revealing the conditions for Fermi to non-Fermi liquid crossover due to Fermi surface warping.

Findings

Self-energy diverges at the Fermi surface, indicating non-Fermi liquid behavior.

Particle-hole processes contribute more strongly to divergence than particle-particle processes.

Crossover from Fermi to non-Fermi liquid behavior is enhanced with increasing interaction strength.

Abstract

Self-energy at zero temperature is investigated up to the third-order of interaction using one-patch model in two dimensions, whose interaction process corresponds to $g_4$-process of $g$-ology model in one dimension. The self-energy $\Sigma^R({\mib k},\epsilon)$ diverges at $\epsilon=\xi_k$, and the contribution from the particle-hole process in third-order self-energy diagrams has a stronger divergence compared to the one from the particle-particle process. This implies that the loop-cancellation in the forward scattering is insufficient due to the effect of the warping of the Fermi surface. The strong energy dependence of the self-energy in the vicinity of $\epsilon=\xi_k$ implies the existence of the crossover from Fermi to non-Fermi liquid behavior as the momentum becomes away from the Fermi momentum, and this crossover is enhanced as interaction becomes stronger.