Path optimization method for the sign problem

Understand

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions.

• Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed.
• In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled.
• When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem.