Lattice QCD on Non-Orientable Manifolds

TL;DR

This paper introduces a novel approach to lattice QCD simulations using non-orientable manifolds, significantly reducing autocorrelation times while approximately preserving translational invariance, and discusses methods to handle complex fermion determinants.

Contribution

It proposes the use of non-orientable manifolds in lattice QCD to improve simulation efficiency and addresses the fermion determinant complexity with two new methods.

Findings

Autocorrelation time is drastically reduced in quenched simulations.

Translational invariance is preserved up to exponentially small corrections.

Two approaches are proposed to handle complex fermion determinants.

Abstract

A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge, when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a non-orientable manifold, and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is, that translational invariance is preserved up to exponentially small corrections. A Dirac-fermion on a non-orientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.