Single-component fermion chain: emergent mode and liquids of bound states

We study the formation of bound states in a single-component Fermi chain with attractive interactions.
The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase (2M phase) with two gapless modes.
We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2M phase with a 2-component ("emegent") Tomonaga-Luttinger liquid theory description.