Complex Langevin dynamics and zeroes of the fermion determinant

Abstract

QCD at nonzero baryon chemical potential suffers from the sign problem, due to the complex quark determinant. Complex Langevin dynamics can provide a solution, provided certain conditions are met. One of these conditions, holomorphicity of the Langevin drift, is absent in QCD since zeroes of the determinant result in a meromorphic drift. We first derive how poles in the drift affect the formal justification of the approach and then explore the various possibilities in simple models. The lessons from these are subsequently applied to both heavy dense QCD and full QCD, and we find that the results obtained show a consistent picture. We conclude that with careful monitoring, the method can be justified a posteriori, even in the presence of meromorphicity.

67 pages, many figures; minor changes, discussion section added, to appear in JHEP

References in corpus (7)

• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Stochastic quantization at finite chemical potential
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Complex Langevin dynamics and zeroes of the fermion determinant
• Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
• Heavy dense QCD and nuclear matter from an effective lattice theory
• The complex Langevin analysis of spontaneous symmetry breaking induced by complex fermion determinant

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