Particle Propagator of Spin Calogero-Sutherland Model

TL;DR

This paper derives explicit expressions for the particle propagator in the spin 1/2 Calogero-Sutherland model for finite and infinite systems, and analyzes the spectral function revealing characteristic power-law singularities.

Contribution

It provides the first explicit derivation of the particle propagator in the thermodynamic limit for this model, enhancing understanding of its spectral properties.

Findings

Spectral function shows power-law singularities.

Explicit expressions valid for finite and infinite systems.

Results align with known features of 1D correlated systems.

Abstract

Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero-Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.