Single particle Green's function in the Calogero-Sutherland model for rational couplings $\beta=p/q$

TL;DR

This paper derives an exact expression for the single particle Green function in the Calogero-Sutherland model at rational couplings using Jack polynomial techniques, providing insights into the model's spectral properties.

Contribution

It presents a novel exact calculation of the Green function for all rational coupling values in the Calogero-Sutherland model, expanding analytical understanding.

Findings

Exact Green function expression for rational couplings

Identification of two types of intermediate states

Results in the thermodynamical limit

Abstract

We derive an exact expression for the single particle Green function in the Calogero-Sutherland model for all rational values of the coupling $\beta$. The calculation is based on Jack polynomial techniques and the results are given in the thermodynamical limit. Two type of intermediate states contribute. The firts one consists of a particle propagating out of the Fermi sea and the second one consists of a particle propagating in one direction, q particles in the opposite direction and p holes.