Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
- 167 Downloads
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). We exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.
KeywordsLattice Quantum Field Theory Nonperturbative Effects
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- M.V. Fedoryuk, The saddle-point method (in Russian), Izdat. Nauka, Moscow Russia (1977).Google Scholar