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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2017
 DOI:
 10.1007/JHEP05(2017)044
 arXiv:
 arXiv:1701.02322
 Bibcode:
 2017JHEP...05..044A
 Keywords:

 Lattice Quantum Field Theory;
 Phase Diagram of QCD;
 High Energy Physics  Lattice;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 67 pages, many figures