Ground-state properties of dilute one-dimensional Bose gas with three-body repulsion

We determined perturbatively the low-energy universal thermodynamics of dilute one-dimensional bosons with the three-body repulsive forces. The final results are presented for the limit of vanishing potential range in terms of three-particle scattering length. An analogue of Tan`s energy theorem for considered system is derived in generic case without assuming weakness of the interparticle interaction. We also obtained an exact identity relating the three-body contact to the energy density.