Hierarchical Trion Formation and Fractionalized Solitons in One Dimension

Abstract

Stabilizing commensurate $2:1$ trions in one-dimensional quantum mixtures is typically hindered by phase separation. Within the conventional density-driven framework, the asymmetric locking mechanism generically couples to a softening density mode, creating a geometric constraint that suppresses the formation of a stable trionic liquid. We demonstrate that correlated kinetics can reorganize the low-energy structure to bypass this instability. Driven by microscopic fermion pair-hopping, the fermions first form an emergent pair liquid. At a $2:1$ filling, the density of the emergent pairs exactly matches the bosons. The low-energy theory is therefore reorganized into an effective symmetric $1:1$ pair-boson mixture. This symmetry decouples the locking mechanism from the softening mode, preempting phase separation and stabilizing a trionic liquid. The reconstructed phase exhibits a correlation hierarchy where only the composite trion retains quasi-long-range order, while the gapped relative sector supports parity-constrained topological kink excitations.