Discrete thermodynamic Bethe ansatz Original Research Article

We propose discrete TBA equations for models with discrete spectrum. We illustrate our construction on the Calogero–Moser model and determine the discrete 2-body TBA function which yields the exact N-body Calogero–Moser thermodynamics. We apply this algorithm to the Lieb–Liniger model in a harmonic well, a model which is relevant for the microscopic description of harmonically trapped Bose–Einstein condensates in one dimension. We find that the discrete TBA reproduces the N-body groundstate energy of the Lieb–Liniger model in a harmonic well at first order in perturbation theory, but corrections do appear at second order.