Anyon-fermion mapping and applications to ultracold gases in tight waveguides

Abstract

The Fermi-Bose mapping method for one-dimensional (1D) 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 TG gas"), and spin-aligned anyon gas with infinite zero-range odd-wave attractions ("anyonic FTG gas"). It is proved that for even $N\ge 4$ there are states of the anyonic FTG gas on a ring, 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.