  Diagonal and off-diagonal properties of 2D solid 4He systems doped with a
quantized vortex have been investigated via the Shadow Path Integral Ground
State method using the fixed-phase approach. The chosen approximate phase
induces the standard Onsager-Feynman flow field. In this approximation the
vortex acts as a static external potential and the resulting Hamiltonian can be
treated exactly with Quantum Monte Carlo methods. The vortex core is found to
sit in an interstitial site and a very weak relaxation of the lattice positions
away from the vortex core position has been observed. Also other properties
like Bragg peaks in the static structure factor or the behavior of vacancies
are very little affected by the presence of the vortex. We have computed also
the one-body density matrix in perfect and defected 4He crystals finding that
the vortex has no sensible effect on the off-diagonal long range tail of the
density matrix. Within the assumed Onsager Feynman phase, we find that a
quantized vortex cannot auto-sustain itself unless a condensate is already
present like when dislocations are present. It remains to be investigated if
backflow can change this conclusion.
