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

TL;DR

This paper investigates methods to mitigate topological freezing in the 2D CP^{N-1} model through open boundary conditions and parallel tempering, showing promising results in reducing autocorrelation times.

Contribution

It introduces and tests open boundary conditions and parallel tempering to address topological freezing in the CP^{N-1} model, demonstrating their effectiveness.

Findings

Open boundary conditions help avoid topological freezing.

Parallel tempering shows promising efficiency improvements.

Autocorrelation times are reduced but still remain large.

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 L\"uscher 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.