New algorithms for finite density QCD

TL;DR

This paper reviews recent advances in complex Langevin and Lefschetz thimble methods, which enable direct simulations of finite density QCD by addressing the sign problem through complexification techniques.

Contribution

It provides a comparative analysis of two promising methods, highlighting recent results and potential for simulating theories with complex measures.

Findings

Complex Langevin method enables full QCD simulations avoiding the sign problem.

Lefschetz thimble approach shows promising results for non-gauge theories.

Both methods rely on complexification of the field manifold.

Abstract

Recent progress of the complex Langevin method and the Lefschetz thimble in connection with the sign problem is reviewed. These methods rely on the complexification of the original field manifold and they allow direct simulations of theories with non-real measures. Similarities and differences of the two approaches are pointed out. Results using the complex Langevin method, which allows simulations to evade the sign problem in full QCD, are presented. Promising results of the thimble approach for non-gauge theories are also discussed.