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 $\delta$-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.