Exact integral equation for the renormalized Fermi surface

TL;DR

This paper derives an exact integral equation for the renormalized Fermi surface in fermionic many-body systems using the functional renormalization group, generalizing the Hartree-Fock approach.

Contribution

It introduces an exact integral equation for the counterterm defining the Fermi surface within the functional RG framework, extending beyond traditional approximations.

Findings

Derivation of an exact integral equation for the Fermi surface

Reduction to Hartree-Fock equation in a simple approximation

Provides a self-consistent method for Fermi surface calculation

Abstract

The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.