Evading the sign problem in random matrix simulations

Abstract

We show how the sign problem occurring in dynamical simulations of random matrices at nonzero chemical potential can be avoided by judiciously combining matrices into subsets. For each subset the sum of fermionic determinants is real and positive such that importance sampling can be used in Monte Carlo simulations. The number of matrices per subset is proportional to the matrix dimension. We measure the chiral condensate and observe that the statistical error is independent of the chemical potential and grows linearly with the matrix dimension, which contrasts strongly with its exponential growth in reweighting methods.

4 pages, 3 figures, minor corrections, as published in Phys. Rev. Lett

References in corpus (5)

• Phase of the Fermion Determinant at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• Random matrix analysis of the QCD sign problem for general topology
• Chiral Condensate at Nonzero Chemical Potential in the Microscopic Limit of QCD
• The QCD sign problem and dynamical simulations of random matrices

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• Solution to sign problems in models of interacting fermions and quantum spins
• Random Matrix Theory and Quantum Chromodynamics
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• Gibbs sampling of complex valued distributions
• Solution to the sign problem in a frustrated quantum impurity model
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• Developments in lattice QCD for matter at high temperature and density
• Positivity of center subsets for QCD
• Diagrammatic representation of scalar QCD and sign problem at nonzero chemical potential
• Representation of complex probabilities and complex Gibbs sampling
• The interplay of the sign problem and the infinite volume limit: gauge theories with a theta term
• Sign problem and subsets in one-dimensional QCD