# Tempered transitions between thimbles

## TL;DR

This paper introduces a tempered transition algorithm to improve Monte Carlo sampling in quantum field theories with complex actions, effectively addressing the sign problem by enabling sampling across multiple modes.

## Contribution

The paper proposes a novel tempered proposals algorithm that enhances sampling efficiency in complex action quantum field theories, building on the holomorphic gradient flow method.

## Key findings

- Tempered proposals successfully sample the 0+1 dimensional Thirring model at finite density.
- The method overcomes the limitations of standard Monte Carlo sampling in multi-modal distributions.
- The approach demonstrates potential for broader applications in complex quantum systems.

## Abstract

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 multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0+1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.