(Para)fermionization in spinor Tonks-Girardeau gases

Abstract

We present a second quantized theory of spinor Tonks-Girardeau (TG) gases using the 1D Hubbard model in the U₀ → +∞ limit. We show that hard-core bosons locally satisfy R-parastatistics, hence the model can be mapped to a system of parafermionic quasiparticles. The mapping results to quasiparticles with infinite lifetimes and preserves the fact that the flavor components do not contribute to the ground state energy. We also show that the emergent parafermion system does not satisfy conventional particle-hole symmetry. These results point to spinor TG gases being potential experimental platforms for verifying the existence of paraparticles.