Diagrammatic Quantum Monte Carlo Algorithm in Momentum Representation: Hess-Fairbank Effect and Mesoscopics in 1D BEC with Attractive Interaction

Abstract

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).