Perturbative correction to the ground-state properties of one-dimensional strongly interacting bosons in a harmonic trap

We calculate the first-order perturbation correction to the ground-state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With c denoting the interaction strength, we find that, for a large number of particles N, the 1/c correction to the ground-state energy increases as N^5/2, in contrast to the unperturbed Tonks-Girardeau value that is proportional to N². We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground-state energy and reproduces the zero temperature thermodynamics obtained by a local-density approximation.