Heavy-dense QCD, sign optimization, and Lefschetz thimbles

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 approach, 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 reweighting 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. Published by the American Physical Society 2024