Anyon-Fermion Mapping and Applications to Ultracold Gases in Tight Waveguides

The Fermi-Bose mapping method for one-dimensional Bose and Fermi gases with zero-range interactions is generalized to an anyon-fermion mapping and applied to exact solution of several models of ultracold gases with anyonic exchange symmetry in tight waveguides: anyonic Calogero-Sutherland model, anyons with point hard-core interaction (anyonic Tonks-Girardeau gas), and spin-aligned anyon gas with infinite zero-range odd-wave attractions (attractive anyonic Tonks-Girardeau, or AATG, gas). It is proved that for even N≥4 there are states of the AATG gas on A, with anyonic phase slips which are odd integral multiples of π/(N-1), of energy lower than that of the corresponding fermionic ground state. A generalization to a spinor Fermi gas state with anyonic symmetry under purely spatial exchange enables energy lowering by the same mechanism