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

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 wave functions 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 wave functions 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 wave function of the inhomogeneous system which well describes the ground state at finite, large, and equal interaction strengths, as validated by numerical simulations.

Locations

• Physical Review A - View
• arXiv (Cornell University) - View - PDF
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