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.

arXiv comment41 pages, 8 figures; extended discussion; 2 new figures, typos corrected

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Cited by in corpus (24)

• Equivariant flow-based sampling for lattice gauge theory
• SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Towards glueball masses of large-$N$ $\mathrm{SU}(N)$ pure-gauge theories without topological freezing
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• Topological critical slowing down: variations on a toy model
• Multicomponent compact Abelian-Higgs lattice models
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Three-dimensional ferromagnetic CP(N-1) models
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Topological sampling through windings
• Towards reduction of autocorrelation in HMC by machine learning
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• Scaling properties of multiscale equilibration
• Topological susceptibility of $2d{\mathrm{CP}}^1$ or $\mathrm{O}(3)$ non-linear $\sigma$-model: is it divergent or not?
• Two-dimensional multicomponent Abelian-Higgs lattice models
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling
• Scaling of Stochastic Normalizing Flows in $\mathrm{SU}(3)$ lattice gauge theory
• Topology changing update algorithms for SU(3) gauge theory
• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence