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

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.

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References in corpus (6)

• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Fractional Statistics in One-Dimension: View From An Exactly Solvable Model
• Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
• Dynamical correlation functions in the Calogero-Sutherland model
• Density Correlation Functions in Calogero Sutherland Models
• Exact calculation of the ground state single-particle Green's function for the $1/r^2$ quantum many body system at integer coupling

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