Many-body properties of quasi-one-dimensional boson gas across a narrow CIR

We study strong interaction effects in a one-dimensional (1D) boson gas across a narrow confinement-induced resonance (CIR). In contrast to the zero-range potential, the 1D two-body interaction in the narrow CIR can be written as a polynomial of derivative δ-function interaction on many-body level. Using the asymptotic Bethe ansatz, we find that the low-energy physics of this many-body problem is described by the Tomonaga-Luttinger liquid where the Luttinger parameters are essentially modified by an effective finite-range parameter v. This parameter drastically alters quantum criticality and universal thermodynamics of the gas. In particular, it drives the Tonks-Girardeau (TG) gas from non-mutual Fermi statistics to mutual statistics or to a more exclusive super-TG gas. This novel feature is further discussed in terms of the breathing mode which is experimentally measurable.