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arXiv:hep-lat/0602018 · Computer Physics Communications

Efficient cluster algorithm for models

Bernard B. Beard, Michele Pepe A, S. Riederer, U.‐J. Wiese

Published Sep 27, 2006• 9 citations
arXivHTMLPDF
DOI
10.1016/j.cpc.2006.06.007

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We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems.Such systems provide a new regularization for CP(N -1) models in the framework of D-theory, which is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantum variables instead of classical fields.Despite several attempts, no efficient cluster algorithm has been constructed for CP(N -1) models in the standard formulation of lattice field theory.In fact, there is even a no-go theorem that prevents the construction of an efficient Wolff-type embedding algorithm.We present various simulations for different correlation lengths, couplings and lattice sizes.We have simulated correlation lengths up to 250 lattice spacings on lattices as large as 640×640 and we detect no evidence for critical slowing down.

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The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.
We construct an efficient cluster algorithm for ferromagnetic SU(N)-symmetric quantum spin systems.Such systems provide a new regularization for CP(N -1) models in the framework of D-theory, which is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantum variables instead of classical fields.Despite several attempts, no efficient cluster algorithm has been constructed for CP(N -1) models in the standard formulation of lattice field theory.In fact, there is even a no-go theorem that prevents the construction of an efficient Wolff-type embedding algorithm.We present various simulations for different correlation lengths, couplings and lattice sizes.We have simulated correlation lengths up to 250 lattice spacings on lattices as large as 640×640 and we detect no evidence for critical slowing down.