Why normal electrons with sufficiently singular interactions do not have a sharp Fermi surface

TL;DR

This paper demonstrates that in Fermi systems with highly singular interactions, the momentum distribution becomes smooth near the Fermi surface, indicating the absence of a sharp Fermi surface in such cases.

Contribution

The authors employ a bosonization approach to show that strong singular interactions lead to an analytic momentum distribution near the Fermi surface, challenging traditional Fermi liquid theory.

Findings

Momentum distribution is analytic near the Fermi surface with singular interactions.

Singular density-density interactions diverging faster than |q|^{-2(d-1)} eliminate the sharp Fermi surface.

Coupling to transverse gauge fields in less than three dimensions also results in a smooth momentum distribution.

Abstract

We use a bosonization approach to show that the momentum distribution $n_{\bf{k}}$ of normal Fermi systems with sufficiently singular interactions is analytic in the vicinity of the non-interacting Fermi surface. These include singular density-density interactions that diverge in $d$ dimensions stronger than $ | {\bf{q}} |^{- 2 (d -1)}$ for vanishing momentum transfer ${\bf{q}}$, but also fermions that are coupled to transverse gauge fields in $ d < 3$.