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

Ken Yokoyama
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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 $Σ^R({\mib k},ε)$ diverges at $ε=ξ_k$, 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 $ε=ξ_k$ 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.

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Ken Yokoyama. 1998-06-12. Crossover from Fermi to Non-Fermi Liquid in Two-Dimensional Interacting Fermions. https://arxiv.org/abs/cond-mat/9806158

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