Simulating low dimensional QCD with Lefschetz thimbles

TL;DR

This paper explores the application of Lefschetz thimbles to simulate low-dimensional QCD, aiming to mitigate the sign problem in non-perturbative lattice calculations at finite baryon density.

Contribution

It demonstrates the use of thimble discretization in (0+1)-dimensional QCD with staggered quarks and discusses potential challenges in extending to higher dimensions.

Findings

Thimble approach alleviates sign problem in simple QCD models.

Application to (0+1)D QCD shows promising results.

Identifies issues for higher-dimensional extensions.

Abstract

Non-perturbative lattice QCD calculations at non vanishing baryon number density are hampered by the QCD sign problem. The path integral, that in lattice QCD is calculated numerically, becomes highly oscillating. One possible solution is the Lefschetz thimble approach. It requires a deformation of the original integration domain into a manifold embedded in complex space. For properly chosen integration manifolds ("thimbles") the sign problem is drastically alleviated. For some bosonic and fermionic models this approach has been shown to work. Here we apply the thimble disretization to (0+1)-dimensional QCD with standard staggerd quarks and disscuss issues that may arrise in higher dimensions.