Parquet solution for a flat Fermi surface

TL;DR

This paper investigates electronic instabilities in systems with flat Fermi surfaces, revealing how different interactions lead to magnetic or superconducting phases, with implications for high-temperature superconductors.

Contribution

It classifies possible instabilities and derives renormalization-group equations for systems with flat Fermi surfaces, extending understanding of phase competition.

Findings

Antiferromagnetic instability dominates with repulsive Hubbard interaction.

Deviations from perfect flatness favor d-wave superconductivity.

Numerical solutions align with ladder approximation results.

Abstract

We study instabilities occurring in the electron system whose Fermi surface has flat regions on its opposite sides. Such a Fermi surface resembles Fermi surfaces of some high-$T_c$ superconductors. In the framework of the parquet approximation, we classify possible instabilities and derive renormalization-group equations that determine the evolution of corresponding susceptibilities with decreasing temperature. Numerical solutions of the parquet equations are found to be in qualitative agreement with a ladder approximation. For the repulsive Hubbard interaction, the antiferromagnetic (spin-density-wave) instability dominates, but when the Fermi surface is not perfectly flat, the $d$-wave superconducting instability takes over.