Many-body soliton-like states of the bosonic ideal gas

We study the lowest energy states for fixed total momentum, i.e. yrast states, of $N$ bosons moving on a ring. As in the paper of A. Syrwid and K. Sacha \cite{syrwid2015} , we compare mean field solitons with the yrast states, being the many-body Lieb-Liniger eigenstates. We show that even in the limit of vanishing interaction the yrast states possess features typical for solitons, like the phase jumps and the density notches. These properties are simply effects of the bosonic symmetrization and are encoded in the Dicke states hidden in the yrast states.