  A novel algorithm of Diagrammatic Quantum Monte Carlo in momentum
representation is reported in details. New models can be studied with this
algorithm. For Bose systems with attractive interaction, the algorithm is free
of the well-known minus-sign problem, while in other models it is weaker than
in real-space methods.
  Using this algorithm, we present the results of an exact numeric simulation
of N one-dimensional bosons with attractive delta-functional interaction in a
rotating ring. We prove that in the large-N limit the system can be described
by conventional methods of weakly interacting gas, the dimensionless parameter
of weak interaction being just 1/N. When the strength of interaction is less
then a certain threshold value, the dependence of angular momentum on the
rotation frequency features plateaus characteristic of the irrotational fluid
(the Hess-Fairbank effect).
