Sign optimization and complex saddle points in one-dimensional QCD

TL;DR

This paper applies sign optimization to one-dimensional QCD at finite density, reducing the fermion sign problem by deforming the integration domain into a complexified space, and relates it to complex saddle points and Lefschetz thimbles.

Contribution

It introduces a novel sign optimization method for one-dimensional QCD using complex domain deformation based on the angular representation of SU(3).

Findings

Reduced phase fluctuations in the path integral.

Connected sign optimization to complex saddle points.

Linked the approach to generalized Lefschetz thimbles.

Abstract

We study one-dimensional QCD at finite quark density by using the sign optimization framework. The fermion sign problem is mitigated by deforming the path integral domain, $SU(3)$ to a complexified one ${\cal M} \subset SL(3)$, explicitly constructed to reduce the phase fluctuations. The complexification is constructed using the angular representation of $SU(3)$. We provide a physical explanation of the optimization procedure in terms of complex saddle points. This picture connects the sign optimization framework to the generalized Lefschetz thimbles.