Fighting topological freezing in the two-dimensional CPN−1 model

We perform Monte Carlo simulations of the CPN−1 model on the square lattice for N = 10, 21, and 41. Our focus is on the severe slowing down related to instantons. To fight this problem we employ open boundary conditions as proposed by Lüscher and Schaefer for lattice QCD. Furthermore we test the efficiency of parallel tempering of a line defect. Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large. The results obtained with parallel tempering are encouraging