Exclusion Statistical TBA and the Quantum Calogero Model

Abstract

Thermodynamics of the quantum Calogero model is studied by the microcanonical ensemble approach. We formulate a thermodynamic Bethe ansatz (TBA), whose reference state is the generalized ideal gas with fractional statistics (free a -on). Using the a -onic TBA, the free-quasiparticle picture for the Calogero model is identified as the free a -on. We calculate the thermodynamic potential and the distribution function for the Calogero model in the thermodynamic limit. The thermodynamic potential at thermal equilibrium can be understood by the Bernoulli equation. We also show that the thermodynamics of the Calogero model and the Sutherland model are the same except for the dispersion relations.