Single Scale Analysis of Many Fermion Systems. Part 1: Insulators

TL;DR

This paper develops a fermionic functional integral approach to analyze insulators with a gap, providing estimates on Green's functions that facilitate future zero-temperature fermion system studies.

Contribution

It introduces a method to estimate Green's functions for gapped fermion systems, laying groundwork for analyzing gapless fermions at zero temperature.

Findings

Green's functions estimates depend on the size of the energy gap

Method enables analysis of fermion systems with a gap

Prepares for zero-temperature fermion system analysis

Abstract

We construct, using fermionic functional integrals, thermodynamic Green's functions for a weakly coupled fermion gas whose Fermi energy lies in a gap. Estimates on the Green's functions are obtained that are characteristic of the size of the gap. This prepares the way for the analysis of single scale renormalization group maps for a system of fermions at temperature zero without a gap.