Regularization of the complex Langevin method

The complex Langevin method, a numerical method used to compute the ensemble average with a complex partition function, often suffers from runaway instability. We study the regularization of the complex Langevin method via augmenting the action with a stabilization term. Since the regularization introduces biases to the numerical result, two approaches, named 2R and 3R methods, are introduced to recover the unbiased result. The 2R method supplements the regularization with regression to estimate the unregularized ensemble average, and the 3R method reduces the computational cost by coupling the regularization with a reweighting strategy before regression. Both methods can be generalized to the SUon thorn theory and are assessed from several perspectives. Several numerical experiments in the lattice field theory are carried out to show the effectiveness of our approaches.

Automated summary

This study investigates the regularization of the complex Langevin method by augmenting the action with a stabilization term and introduces two methods to recover unbiased results. These methods are assessed in SU(X) thorn theory and demonstrate effectiveness through numerical experiments in lattice field theory.