Abstract
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.
Highlights
The CPN−1 model shares fundamental properties such as asymptotic freedom and confinement with QCD
Our results for open boundary conditions are consistent with the expectation that topological freezing is avoided, while autocorrelation times are still large
We have shown that the severe slowing down in the simulation of the lattice CPN−1 model can be avoided by using open boundary conditions in one of the directions
Summary
The CPN−1 model shares fundamental properties such as asymptotic freedom and confinement with QCD. It turned out that these topological objects pose a particular problem in the simulation of the lattice CPN−1 model, similar to lattice QCD. The numerical studies show that in the case of the CPN−1 model the problem becomes worse with increasing N. Since it is much less expensive to simulate the twodimensional model than lattice QCD, it is a good test bed for new ideas and algorithms that could overcome the severe slowing down of the topological modes. Since the CPN−1 model is much cheaper to simulate than lattice QCD, a larger range of lattice spacings can be studied and autocorrelation functions can be computed more accurately. We like to mention that for the CPN−1 model dual formulations can be found These can be simulated by using the worm algorithm [20, 21]. In these dual formulations there are no topological sectors and severe slowing down does not occur in the simulation
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