Roton in a many-body dipolar system

We solve exactly the many-body 1D model of atoms interacting via short range attractive and long range repulsive dipole-dipole forces. Periodic boundary conditions imply the conservation of total momentum. We find that the so called yrast states, i.e. the lowest energy states with the fixed total momentum, may contain elementary excitations known from the Bogoliubov approximation. In particular, we identify the celebrated roton state. With our exact methods we also go to stronger interactions, beyond the validity of Bogoliubov approximation.