Theory of many-fermion systems II: The case of Coulomb interactions

TL;DR

This paper extends a field-theoretical framework to disordered electron systems with Coulomb interactions, deriving a nonlinear sigma model and analyzing soft modes via Ward identities.

Contribution

It introduces a generalized nonlinear sigma model for Coulomb-interacting disordered electrons, expanding previous short-range interaction theories.

Findings

Derivation of the generalized nonlinear sigma model for Coulomb interactions

Analysis of Ward identities controlling soft modes

Discussion of implications for disordered electron systems

Abstract

In a recent paper (cond-mat/9703164) a general field-theoretical description of many-fermion systems with short-ranged interactions has been developed. Here we extend this theory to the case of disordered electrons interacting via a Coulomb potential. A detailed discussion is given of the Ward identity that controls the soft modes in the system, and the generalized nonlinear sigma model for the Coulombic case is derived and discussed.