The effect of Fermi surface curvature on low-energy properties of fermions with singular interactions

TL;DR

This paper investigates how Fermi surface curvature influences the low-energy behavior of two-dimensional fermions with singular interactions, comparing multi-dimensional bosonization and Eliashberg approaches to identify necessary methodological extensions.

Contribution

It reveals that extending multi-dimensional bosonization is essential for consistent predictions with Eliashberg theory in systems with Fermi surface curvature.

Findings

Agreement between methods requires extending bosonization techniques.

Fermi surface curvature significantly affects low-energy fermion properties.

Comparison clarifies limitations of existing theoretical approaches.

Abstract

We discuss the effect of Fermi surface curvature on long-distance/time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge field-like propagator. By comparing the predictions based on the idea of multi-dimensional bosonization with those of the strong- coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.