An exact method for bosonizing the Fermi surface in arbitrary dimensions

TL;DR

This paper presents an exact and straightforward bosonization method for non-interacting fermionic systems with Fermi surfaces in any dimension, connecting microscopic Hamiltonians to effective bosonic theories.

Contribution

It introduces a rigorous, exact bosonization technique applicable to arbitrary dimensions, including diagrammatic rules for correlation functions and analysis of interactions.

Findings

Derived an exact bosonization method matching previous long-wavelength results.

Developed diagrammatic rules for correlation function calculations.

Showed that the simplest approximation reproduces RPA results.

Abstract

Inspired by the recent work by Delacretaz et. al., we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we show that the derived bosonized action is exactly equivalent to the action obtained by Delacretaz et. al. In addition, we propose diagrammatic rules to evaluate correlation functions using our bosonized theory and demonstrate these rules by calculating the three- and four-point density correlation functions. We also consider a general density-density interaction and show that the simplest approximation in our bosonic theory is identical to RPA results.