Worm Algorithm for CP(N-1) Model

TL;DR

This paper introduces an efficient worm algorithm for simulating the 2D CP(N-1) model on the lattice, enabling studies at finite density with improved computational performance and insights into different lattice actions.

Contribution

The paper presents a novel worm algorithm suitable for the lattice CP(N-1) model in a dual flux-variables representation, including internal variable moves for faster Monte Carlo simulations.

Findings

The algorithm effectively simulates the CP(N-1) model at finite density.

Marked differences observed in continuum limit approaches between two lattice actions.

Enhanced Monte Carlo efficiency through internal variable space moves.

Abstract

The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D CP(N-1) on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice CP(N-1) model has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular CP(N-1) lattice actions and exhibit marked differences in their approach to the continuum limit.