Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases

TL;DR

This paper provides an exact analytical solution for strongly interacting quasi-one-dimensional spin-1 bosons, revealing a duality with non-interacting fermions and spins, and analyzing their energy spectrum and momentum distribution.

Contribution

It introduces an exact solution for spinor Bose gases with infinite delta-repulsion, extending Girardeau's Fermi-Bose mapping to include spin degrees of freedom.

Findings

Spinor bosons behave like a combination of non-interacting fermions and distinguishable spins.

The momentum distribution depends on the symmetry of the spin wave function.

The ground state multiplet splits in the regime of large but finite repulsion.

Abstract

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.