Single-particle Green's functions of the Calogero-Sutherland model at couplings \lambda = 1/2, 1, and 2

TL;DR

This paper derives exact integral representations for the two-particle Green's function of the Calogero-Sutherland model at specific couplings, revealing fractionalization effects in the single-particle Green's function.

Contribution

It introduces a novel application of superanalytic techniques to derive exact Green's functions for the CSM at special couplings, including fractionalization phenomena.

Findings

Exact integral representations for two-particle Green's functions.

Closed-form expressions for single-particle Green's functions.

Identification of fractionalization contributions in Green's functions.

Abstract

At coupling strengths lambda = 1/2, 1, or 2, the Calogero-Sutherland model (CSM) is related to Brownian motion in a Wigner-Dyson random matrix ensemble with orthogonal, unitary, or symplectic symmetry. Using this relation in conjunction with superanalytic techniques developed in mesoscopic conductor physics, we derive an exact integral representation for the CSM two-particle Green's function in the thermodynamic limit. Simple closed expressions for the single-particle Green's functions are extracted by separation of points. For the advanced part, where a particle is added to the ground state and later removed, a sum of two contributions is found: the expected one with just one particle excitation present, plus an extra term arising from fractionalization of the single particle into a number of elementary particle and hole excitations.