Stability of complex Langevin dynamics in effective models

Understand

The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations.

• Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution.
• Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model.
• Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics.