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We investigate the formation of self-bound quantum droplets in aone-dimensional binary mixture of bosonic atoms, applying the method ofnumerical diagonalization of the full Hamiltonian. The excitation spectra andground-state pair correlations signal the formation of a few-boson droplet whencrossing the region of critical inter-species interactions. The self-bindingaffects the rotational excitations, displaying a change in the energydispersion from negative curvature, associated with superfluidity in themany-body limit, to a nearly parabolic curvature indicative of rigid bodyrotation. We exploit two global symmetries of the system to further analyze thefew-body modes in terms of transition matrix elements and breathing modedynamics. The exact results are compared to the usual ad-hoc inclusion ofhigher-order contributions in the extended Gross-Pitaevskii equation, showing aremarkable agreement between the few-body regime and the thermodynamic limit inone dimension.

Superfluid-droplet crossover in a binary boson mixture on a ring: Exact diagonalization solutions for few-particle systems in one dimension