Heavy-dense QCD, sign optimization and Lefschetz thimbles

TL;DR

This paper investigates the heavy-dense limit of lattice QCD at high density, employing sign optimization and Lefschetz thimbles to mitigate the sign problem and improve simulation accuracy.

Contribution

It introduces a sign optimization method that deforms the integration domain in complex space, effectively reducing the sign problem in heavy-dense QCD simulations.

Findings

Sign optimization mitigates the sign problem at large volumes.

The complex manifold from sign optimization overlaps with Lefschetz thimbles.

The method enables simulations where re-weighting fails.

Abstract

We study the heavy-dense limit of QCD on the lattice with heavy quarks at high density. The effective three dimensional theory has a sign problem which is alleviated by sign optimization where the path integration domain is deformed in complex space in a way that minimizes the phase oscillations. We simulate the theory via a Hybrid-Monte-Carlo, for different volumes, both to leading order and next-to-next-to leading order in the hopping expansion, and show that sign optimization successfully mitigates the sign problem at large enough volumes where usual re-weighting methods fail. Finally we show that there is a significant overlap between the complex manifold generated by sign optimization and the Lefschetz thimbles associated with the theory.