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arXiv:hep-th/9508115 · Nuclear Physics B

Single-particle Green function in the Calogero-Sutherland model for rational couplings β = p/q

Didina Serban, Frédéric Lesage, Vincent Pasquier

Published May 1, 1996• 19 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(96)00071-5

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At coupling strengths \ensuremath{\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.
One-dimensional model of nonrelativistic particles with inverse-square interaction potential known as the Calogero-Sutherland model is shown to possess fractional statistics. Using the theory of Jack polynomials the exact dynamical density-density correlation function and the hole propagator part of one-particle Green's function at any rational interaction coupling constant are obtained and used to show clear evidences of the fractional exclusion statistics in the sense of Haldane's "generalized Pauli exclusion principle." This model is also endowed with the corresponding natural exchange statistics.