Exact solution for infinitely strongly interacting Fermi gases in tight waveguides

TL;DR

This paper provides an exact analytical solution for strongly interacting spin-1/2 fermions in one-dimensional waveguides, revealing detailed density profiles and spin state behaviors under infinite repulsion.

Contribution

It introduces a novel method combining boundary conditions and group theory to solve for eigenstates of strongly interacting fermions with arbitrary confinement.

Findings

Ground-state density resembles polarized noninteracting fermions

Spin-dependent densities vary with spin configurations

Ground state splitting occurs at large but finite repulsion

Abstract

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-1/2 fermions with infinite repulsion for arbitrary confining potential. The eigenfunctions are constructed by the combination of Gireardeau's hard-core contacting boundary condition and group theoretical method which guarantees the obtained states to be simultaneously the eigenstates of $S$ and $S_z$ and fulfill the antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.