Quantum Monte-Carlo simulation of the phase transition in a two – dimensional quantum Josephson system

Path Integral Quantum Monte Carlo simulation is used to study properties of 2D quanturn Josephson array and other systems, described by $2+1$ XY model. Optimal methods of simulations are considered. The phase diagram of the system in the plane temperature $T$ – dimensionless quantum parameter $q$ ($q=\hbar/\sqrt{JC}$), $J$ is the Josephson coupling constant, $C$ is the intragrain capacitance) is studied in detail. The variational method of the vorticity modulus calculating, which is specific to the topological phase transition, is developed. Analysis of the correlation function of phases, vorticity and helicity moduli leads to the conclusion that the whole line of phase transition is of Kosterlitz–Thouless type.