  The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it
possesses confinement, asymptotic freedom and a non-trivial vacuum structure.
Due to the lower dimensionality and the absence of fermions, the computational
cost for simulating 2D CP(N-1) on the lattice is much lower than that for
simulating 4D QCD. However, to our knowledge, no efficient algorithm for
simulating the lattice CP(N-1) model has been tested so far, which also works
at finite density. To this end we propose a new type of worm algorithm which is
appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables
based representation, in which the introduction of a chemical potential does
not give rise to any complications. In addition to the usual worm moves where a
defect is just moved from one lattice site to the next, our algorithm
additionally allows for worm-type moves in the internal variable space of
single links, which accelerates the Monte Carlo evolution. We use our algorithm
to compare the two popular CP(N-1) lattice actions and exhibit marked
differences in their approach to the continuum limit.
