Fighting topological freezing in the two-dimensional C P N − 1 model

D’Elia

2021

J. High Energ. Phys.

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 CPN–1 models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time of Q2 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 b2, reaching an accuracy comparable with that of the large-N limit of the topological susceptibility.

Section: Jhep03(2021)111mentioning

confidence: 99%

“…To mitigate this problem, we adopt, in this work, the parallel tempering algorithm proposed for the CP N −1 models in ref. [52], where this algorithm has been shown to perform as well as simulations with open boundaries while bypassing their complications related to finite-size effects. Moreover, as shown for CP N −1 models in ref.…”

Section: Jhep03(2021)111mentioning

confidence: 99%

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

Bonanno

D’Elia

2021

J. High Energ. Phys.

“…Given these premises it is natural to think that the critical slowing down of the topological susceptibility could be alleviated by using different boundary conditions, that do not constraint the winding number to be integer (or almost integer). This idea was put forward in [73], where the use of open boundary condition was suggested, and some interesting variations on the same theme can be found in [74,75].…”

Section: Variation 4: Open Boundary Conditionsmentioning

confidence: 99%

Topological critical slowing down: Variations on a toy model

D’Elia

2018

Phys. Rev. E

Numerical simulations of lattice quantum field theories whose continuum counterparts possess classical solutions with nontrivial topology face a severe critical slowing down as the continuum limit is approached. Standard Monte Carlo algorithms develop a loss of ergodicity, with the system remaining frozen in configurations with fixed topology. We analyze the problem in a simple toy model, consisting of the path integral formulation of a quantum mechanical particle constrained to move on a circumference. More specifically, we implement for this toy model various techniques which have been proposed to solve or alleviate the problem for more complex systems, like non-Abelian gauge theories, and compare them both in the regime of low temperature and in that of very high temperature. Among the various techniques, we propose an alternative algorithm which completely solves the freezing problem, but unfortunately is specifically tailored for this particular model and not easily exportable to more complex systems.

“…It is however well known that Monte Carlo algorithms typically used in numerical simulations suffer from a severe critical slowing down as the continuum limit is approached, with autocorrelation times of topological observables that grow about exponentially in the inverse of the lattice spacing [10][11][12][13]. This led to the development of new algorithms, specifically devised to improve the sampling of topologically nontrivial configuration [7,8,[14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Topological susceptibility of two-dimensional U(N) gauge theories

Rossi

2019

Phys. Rev. D

In this paper we study the topological susceptibility of two-dimensional U (N ) gauge theories. We provide explicit expressions for the partition function and the topological susceptibility at finite lattice spacing and finite volume. We then examine the particularly simple case of the abelian U (1) theory, the continuum limit, the infinite volume limit, and we finally discuss the large N limit of our results.