Worm Algorithm for CP(N-1) Model

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.

45 pages, 16 figures

References in corpus (6)

• Worm algorithms for classical statistical models
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Simulating the All-Order Strong Coupling Expansion IV: CP(N-1) as a loop model
• Sampling of General Correlators in Worm Algorithm-based Simulations
• Precision study of critical slowing down in lattice simulations of the CP^{N-1} model
• Topological charge on the lattice: a field theoretical view of the geometrical approach

Cited by in corpus (11)

• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• Image-processing the topological charge density in the CP(N-1) model
• Remarks on the construction of worm algorithms for lattice field theories in worldline representation
• Diagrammatic Monte-Carlo for weak-coupling expansion of non-Abelian lattice field theories: large-N U(N)xU(N) principal chiral model
• Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles
• Phase diagram of the two-dimensional O(3) model from dual lattice simulations
• A Worm Algorithm for the Lattice CP(N-1) Model
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model