Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model

Abstract

We perform Monte Carlo simulations of the CP${}^{N-1}$ 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 in 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.

41 pages, 8 figures; extended discussion; 2 new figures, typos corrected

References in corpus (6)

• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• A local factorization of the fermion determinant in lattice QCD
• Diffusion of topological charge in lattice QCD simulations
• Worm Algorithm for CP(N-1) Model

Cited by in corpus (6)

• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Towards reduction of autocorrelation in HMC by machine learning
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Two-dimensional multicomponent Abelian-Higgs lattice models