A complex path around the sign problem

TL;DR

This paper reviews recent methods that address the sign problem in Monte Carlo simulations by complexifying the integration path, discussing theoretical, algorithmic aspects and presenting results in low-dimensional field theories.

Contribution

It provides a comprehensive review of complex contour deformation techniques to mitigate the sign problem in Monte Carlo calculations, including theoretical foundations and algorithmic challenges.

Findings

Successful application to low-dimensional field theories

Insights into the theoretical basis of contour deformation methods

Discussion of algorithmic issues and potential solutions

Abstract

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.