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The information content of continuous quantum variables systems is usuallystudied using a number of well known approximation methods. The approximationsare made to obtain the spectrum, eigenfunctions or the reduced density matricesthat are essential to calculate the entropy-like quantities that quantify theinformation. Even in the sparse cases where the spectrum and eigenfunctions areexactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduceddensity matrices that characterize the problem, must be obtained in anapproximate fashion. In this work, we obtain analytically a finiterepresentation of the reduced density matrices of the fundamental state of theN-particle Calogero model for a discrete set of values of the interactionparameter. As a consequence, the exact entanglement spectrum and von Neumannentropy is worked out.

Exact finite reduced density matrix and von Neumann entropy for the Calogero model