Jacques Bloch - Academia.edu (original) (raw)
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Papers by Jacques Bloch
EPJ Web of Conferences
We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the co... more We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.
Journal of High Energy Physics, 2013
We present a subset method which solves the sign problem for QCD at nonzero quark chemical potent... more We present a subset method which solves the sign problem for QCD at nonzero quark chemical potential in 0+1 dimensions. The subsets gather gauge configurations based on the center symmetry of the SU(3) group. We show that the sign problem is solved for one to five quark flavors and that it slowly reappears for a larger number of flavors. We formulate an extension of the center subsets that solves the sign problem for a larger number of flavors as well. We also derive some new analytical results for this toy model.
Physical Review D, 2012
We present a solution to the sign problem in dynamical random matrix simulations of a twomatrix m... more We present a solution to the sign problem in dynamical random matrix simulations of a twomatrix 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. A detailed 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 show a 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.
EPJ Web of Conferences
We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the co... more We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.
Journal of High Energy Physics, 2013
We present a subset method which solves the sign problem for QCD at nonzero quark chemical potent... more We present a subset method which solves the sign problem for QCD at nonzero quark chemical potential in 0+1 dimensions. The subsets gather gauge configurations based on the center symmetry of the SU(3) group. We show that the sign problem is solved for one to five quark flavors and that it slowly reappears for a larger number of flavors. We formulate an extension of the center subsets that solves the sign problem for a larger number of flavors as well. We also derive some new analytical results for this toy model.
Physical Review D, 2012
We present a solution to the sign problem in dynamical random matrix simulations of a twomatrix m... more We present a solution to the sign problem in dynamical random matrix simulations of a twomatrix 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. A detailed 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 show a 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.