The QCD sign problem and dynamical simulations of random matrices

Abstract

At nonzero quark chemical potential dynamical lattice simulations of QCD are hindered by the sign problem caused by the complex fermion determinant. The severity of the sign problem can be assessed by the average phase of the fermion determinant. In an earlier paper we derived a formula for the microscopic limit of the average phase for general topology using chiral random matrix theory. In the current paper we present an alternative derivation of the same quantity, leading to a simpler expression which is also calculable for finite-sized matrices, away from the microscopic limit. We explicitly prove the equivalence of the old and new results in the microscopic limit. The results for finite-sized matrices illustrate the convergence towards the microscopic limit. We compare the analytical results with dynamical random matrix simulations, where various reweighting methods are used to circumvent the sign problem. We discuss the pros and cons of these reweighting methods.

34 pages, 3 figures, references added, as published in JHEP

References in corpus (9)

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• Random Matrix Theory and Chiral Symmetry in QCD
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Cited by in corpus (4)

• Evading the sign problem in random matrix simulations
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• A practical solution to the sign problem in a matrix model for dynamical compactification
• A subset solution to the sign problem in random matrix simulations