Complete series for the off-diagonal correlations of a one-dimensional interacting Bose gas

We use a regularized harmonic-fluid approach, based on the effective low-energy Luttinger-liquid Hamiltonian, for a one-dimensional Bose gas with repulsive contact interactions to compute the complete series corresponding to the large-distance off-diagonal behavior of the one-body density matrix for any value of the Luttinger parameter K. We compare our results with the exact ones known in the Tonks-Girardeau limit of infinitely large interactions (corresponding to K=1), and different from the usual harmonic-fluid approach, we recover the full structure of the series. The structure is conserved for arbitrary values of the interaction strength with power laws fixed by the universal parameter K and a sequence of subleading corrections.