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

TL;DR

This paper generalizes the Fermi-Bose mapping to an anyon-fermion mapping for 1D ultracold gases, enabling exact solutions for models with anyonic exchange symmetry and revealing new energy-lowering states.

Contribution

It introduces an anyon-fermion mapping for 1D gases and applies it to solve models with anyonic symmetry, uncovering novel states with lower energy.

Findings

Existence of lower-energy states with odd multiple phase slips.

Exact solutions for anyonic Calogero-Sutherland and TG gases.

Energy lowering mechanisms in anyonic FTG and spinor Fermi gases.

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 $\pi/(N-1)$, 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.