Numerical sign problem: Difference between revisions

Revision as of 19:07, 5 December 2012

Revision as of 20:55, 14 December 2012

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There are various proposals for solving systems with a severe sign problem:

* Meron-cluster algorithms. These achieve an exponential speed-up by decomposing the fermion world lines in tointo clusters that contribute independently. Cluster algorithms have been developed for certain theories,<ref name='Wiese-cluster'>S. Chandrasekharan and U.-J. Wiese, "Meron-Cluster Solution of Fermion Sign Problems", [http://prl.aps.org/abstract/PRL/v83/i16/p3116_1 Phys. Rev. Lett. 83, 3116–3119 (1999)] [http://arxiv.org/abs/cond-mat/9902128 arXiv:cond-mat/9902128]</ref> but not for the Hubbard model of electrons, nor for [[QCD]], the theory of quarks.

* Stochastic quantization. The sum over configurations is obtained as the equilibrium distribution of states explored by a complex [[Langevin equation]]. So far, the algorithm has been found to evade the sign problem in test models that have a sign problem but do not involve fermions.<ref>G. Aarts, "Can stochastic quantization evade the sign problem? The relativistic Bose gas at finite chemical potential", [http://prl.aps.org/abstract/PRL/v102/i13/e131601 Phys. Rev. Lett. 102, 131601 (2009)], [http://arxiv.org/abs/0810.2089 arXiv:0810.2089]</ref>