Gibbs sampling of complex valued distributions

TL;DR

This paper introduces a novel Monte Carlo sampling method for complex-valued distributions using a heat bath approach with positive complex-plane representations, demonstrating effectiveness on lattice models with complex couplings.

Contribution

It presents a new sampling technique for complex distributions based on positive complex-plane representations, improving upon existing methods like reweighting and complex Langevin.

Findings

Method works for moderate complex couplings

Reproduces results of reweighting and complex Langevin

Fulfills Schwinger-Dyson relations

Abstract

A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane. Efficient ways to construct such representations are also introduced. The performance of the algorithm is tested on small and large lattices with a $\lambda\phi^4$ theory with quadratic nearest-neighbor complex coupling. The method works for moderate complex couplings, reproducing reweighting and complex Langevin results and fulfilling various Schwinger-Dyson relations.