Gibbs sampling of complex valued distributions

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 $\lambda {\varphi }^4$ 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.

23 pages, 2 tables, 11 figure. Major revision

References in corpus (7)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Complex Langevin Equations and Schwinger-Dyson Equations
• Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function
• Existence of positive representations for complex weights
• Beyond complex Langevin equations II: a positive representation of Feynman path integrals directly in the Minkowski time

Cited by in corpus (9)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Status of Complex Langevin
• Does the complex Langevin method give unbiased results?
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Schwinger-Dyson equations and line integrals
• Positive Representations of a Class of Complex Measures
• Explicit positive representation for weights on $R^d$
• Positive representations of complex distributions on groups