Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model

We investigate the higher repulsive branches of one-dimensional (1D) bosonic and fermionic quantum gases beyond the super-Tonks-Girardeau regime, utilizing the Bethe-Ansatz method and exact diagonalization of small trapped clusters. In contrast to the well-studied lowest branches that are characterized by spin-charge separation, we demonstrate the emergence of strong spin-charge correlation in all higher branches with hard-core interactions. This manifests in distinct quasi-momentum distributions and energy spectra for bosons and spin-1/2 fermions, despite their fermionization. Furthermore, trapped fermions in higher branches exhibit novel spin textures, intricately linked to charge excitations, necessitating a coupled multi-chain description beyond single effective spin-chain models. Our findings unveil a rich interplay between spin and charge degrees of freedom in highly excited 1D systems, opening avenues for exploring novel quantum phenomena beyond the conventional paradigm of low-lying states.