Complex paths around the sign problem

Andrei Alexandru, Gökçe Başar, Paulo F. Bedaque, and Neill C. Warrington
Rev. Mod. Phys. 94, 015006 – Published 9 March 2022

Abstract

The Monte Carlo evaluation of path integrals is one of a few general purpose methods to approach strongly coupled systems. It is used in all branches of physics, from QCD and nuclear physics to the correlated electron systems. However, many systems of great importance (dense matter inside neutron stars, the repulsive Hubbard model away from half filling, and dynamical and nonequilibrium observables) are not amenable to the Monte Carlo method as it currently stands due to the so-called sign problem. A new set of ideas recently developed to tackle the sign problem based on the complexification of field space and the Picard-Lefshetz theory accompanying it is reviewed. The mathematical ideas underpinning this approach, as well as the algorithms developed thus far, are described together with nontrivial examples where the method has already been proved successful. Directions of future work, including the burgeoning use of machine learning techniques, are delineated.

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  • Received 29 June 2020

DOI:https://doi.org/10.1103/RevModPhys.94.015006

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Nuclear Physics

Authors & Affiliations

Andrei Alexandru*

  • Department of Physics, The George Washington University, Washington, D.C. 20052, USA

Gökçe Başar

  • Department of Physics, University of North Carolina, Chapel Hill, North Carolina 27599, USA

Paulo F. Bedaque

  • Department of Physics, University of Maryland, College Park, Maryland 20742, USA

Neill C. Warrington§

  • Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195, USA

  • *aalexan@gwu.edu
  • basar@unc.edu
  • bedaque@umd.edu
  • §ncwarrin@umd.edu

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Issue

Vol. 94, Iss. 1 — January - March 2022

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