Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture

TL;DR

This paper provides an exact analytical solution for the ground-state wavefunctions of a strongly interacting one-dimensional Bose-Fermi mixture, revealing how symmetry influences physical properties and proposing an approximate wavefunction for finite interactions.

Contribution

It introduces a generalized Bose-Fermi mapping to solve the degenerate ground-state manifold and characterizes solutions based on symmetry considerations.

Findings

Density profile depends on wavefunction symmetry

Momentum distribution varies with symmetry

Proposed an analytic wavefunction for finite interaction strengths

Abstract

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations.