  We study the attractive Fermi mixture of a
${}^{6}\mathrm{Li}$-${}^{40}\mathrm{K}$ gas in one dimension using the
continuous matrix product states variational ansatz and obtain the $T=0$ phase
diagram. We predict an axial density profile that contains four distinct phases
trapped induced along one-dimensional (1D) tubes, which is more intricate than
those observed in 1D mass-balanced systems or in higher-dimensional gas clouds.
The parameter regimes explored are realistic in view of possible future
experiments. This an application of continuous matrix product states to a
nonintegrable fermionic system.
