Abstract
The CPN−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 CPN−1 on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice CPN−1 model for N>2 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 CPN−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 CPN−1 lattice actions and exhibit marked differences in their approach to the continuum limit.
Highlights
The classical CPN−1 model was introduced in 1978 in different contexts [1,2,3]
A cluster algorithm for the CPN−1 model was proposed in [9] and tested for N = 4, 5, but in contrast to the Ising or to O (N) models, where cluster algorithms solve the critical slowing-down problem almost completely, it was found that for CPN−1, the cluster algorithm does not help in overcoming critical slowing-down, which would be necessary in order to perform further non-perturbative checks of the large N and continuum predictions
We looked at the two most common lattice formulations of the CPN−1 model (referred to as quartic and auxiliary U (1) version, respectively), and reviewed two possibilities how the corresponding partition functions can be expressed in terms of integer valued flux-variables by integrating out the original degrees of freedom
Summary
The two-dimensional quantum theory was discussed independently in [4] and [5], where it was shown that (among other interesting properties) the model possesses a non-trivial. The two-dimensional CPN−1 model is presumably the simplest model which possesses all of these properties and is an ideal toy model to study their interrelations. After the model was studied perturbatively [4,5] and by means of a 1/N expansion in the continuum [4,5,7] and on the lattice [6,7] as well as by means of a strong coupling expansion [10], a crosscheck of some predictions by direct Monte Carlo simulations was attempted in [8].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
