Correct jump design for complex Langevin simulations with fermions

Determine the correct jump construction for complex Langevin simulations with fermions, where the action is complex and no Metropolis accept-reject test is available, in order to maneuver the sampler away from exceptional points and address non-ergodic sampling.

Background

The paper motivates jump-diffusion stochastic quantization partly through the problem of ergodicity loss in complex Langevin simulations with fermions. In such simulations, singularities in the complex plane can cause the sampling process to become non-ergodic.

For the real Euclidean actions studied in the paper, jump proposals can be balanced using a Metropolis accept-reject step. That mechanism is unavailable when the action is complex, so the paper identifies the design of jumps that preserve correct sampling in this setting as an unresolved research problem.