Ward type identities for the 2d Anderson model at weak disorder

TL;DR

This paper leverages momentum conservation in 2D to reformulate the Anderson model, revealing that Ward identities constrain electron loops, which could facilitate analysis of weak-coupling regimes.

Contribution

It introduces a novel approach using Ward identities in 2D Anderson models to control electron loops at weak disorder.

Findings

Electron loops are smaller than expected due to Ward identities.

The reformulation aids in studying the weak-coupling regime.

Momentum conservation laws are crucial for the analysis.

Abstract

Using the particular momentum conservation laws in dimension d=2, we can rewrite the Anderson model in terms of low momentum long range fields, at the price of introducing electron loops. The corresponding loops satisfy a Ward type identity, hence are much smaller than expected. This fact should be useful for a study of the weak-coupling model in the middle of the spectrum of the free Hamiltonian.