Split Fermi seas in one-dimensional Bose fluids

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to splitting the ground-state Fermi-sea-like quantum number configuration, are zero-entropy states which display interesting properties more normally associated with ground states. Using a numerically exact method based on integrability, we study these states' excitation spectrum, density correlations, and momentum distribution functions. These correlations display power-law asymptotics and are shown to be accurately described by an effective multicomponent Tomonaga-Luttinger liquid theory whose parameters are obtained from the Bethe ansatz. The nonuniversal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.