From the ubiquitous baryonic matter to superconductivity, studies of matter comprised of bound states of fermions span many branches of physics. Here, we study bound states form among fermions of the same species (in contrast to baryons and conventional Cooper pairing), in a one dimensional setting. Specifically, we study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG, shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We argue that the latter phase consists of a charged and an emergent neutral mode--and that all other bound-state phases (single, pair, trion, etc.) are descendants of this two-mode-phase.
