Bloch, Jacques (2012) A subset solution to the sign problem in random matrix simulations. PHYSICAL REVIEW D, 86 (7): 074505. ISSN 2470-0010, 2470-0029
Full text not available from this repository.Abstract
We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. Adetailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only showa mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-DENSITY; QCD; SPECTRA; LIMIT; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 May 2020 06:49 |
| Last Modified: | 05 May 2020 06:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/17954 |
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