Confined coherence and analytic properties of Green's functions

TL;DR

This paper investigates the pole structure of Green's functions in a simple electron model, challenging previous claims about unphysical pole crossings and discussing implications for confined coherence in quantum systems.

Contribution

It demonstrates that poles of Green's functions can cross the imaginary axis, countering recent assertions, and analyzes the implications for confined coherence in fermionic systems.

Findings

Poles in Green's functions can cross the imaginary axis.

The model's Green's function resembles that of coupled Luttinger liquids.

No definitive conclusions on confined coherence from pole locations.

Abstract

A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a function of the system parameters. The poles in the exact Green's function can cross the imaginary axis, in contrast to recent claims that such a behaviour is unphysical. As the Green's function of the model has the same functional form as an approximate Green's function of coupled Luttinger liquids no definite conclusions concerning the concept of "confined coherence" can be drawn from the locations of the poles of this Green's function.