Split Fermi seas in one-dimensional Bose fluids

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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 to 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 Bethe Ansatz. The non-universal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.