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arXiv:cond-mat/9908290 · Journal of Physics A Mathematical and General

Dynamical correlation functions of the spin Calogero-Sutherland model

Takashi Yamamoto, Mitsuhiro Arikawa

Published Jan 1, 1999• 7 citations
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Abstract

The thermodynamic limit of the dynamical density and spin-density two-point correlation functions for the spin Calogero-Sutherland model are derived from Uglov's finite-size results. The resultant formula for the density two-point correlation function is consistent with the previous conjecture on the basis of the minimal number of elementary excitations.

DOI
10.1088/0305-4470/32/18/309

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The thermodynamic limit of the dynamical density and spin-density two-point correlation functions for the spin Calogero-Sutherland model are derived from Uglov's finite-size results. The resultant formula for the density two-point correlation function is consistent with the previous conjecture on the basis of the minimal number of elementary excitations.
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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.
Spin generalization of the relativistic Calogero - Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry . The spinless model is exactly diagonalized by means of the Macdonald symmetric polynomials. The dynamical density - density correlation function, as well as the one-particle Green function, are evaluated exactly. We also investigate the finite-size scaling of the model and show that the low-energy behaviour is described by the C = 1 Gaussian theory with a new selection rule. The results indicate that the excitations obey the fractional exclusion statistics and also exhibit the Tomonaga - Luttinger liquid behaviour.