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arXiv 2012.140002020-12hep-lat

Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing

Claudio Bonanno, Claudio Bonati, Massimo D'Elia

备注：: 11 pages, 9 eps figures, minor changes and few typos corrected
DOI：: 10.1007/JHEP03(2021)111

英文摘要：

We simulate $4d$ $SU(N)$ pure-gauge theories at large $N$ using a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for $2d$ $CP^{N-1}$ models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of $Q^2$ up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginary $θ$ we are able to refine state-of-the-art results for the large-$N$ behavior of the quartic coefficient of the $θ$-dependence of the vacuum energy $b_2$, reaching an accuracy comparable with that of the large-$N$ limit of the topological susceptibility.

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