Tempered transitions between thimbles

Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multimodal and standard Monte Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the Thirring 0 + 1-dimensional model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.