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

Understand

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 in a line defect.