Simulation of full QCD using overlap fermions

Abstract

Most lattice Quantum Chromodynamics (QCD) formulations explicitly break chiral symmetry. This leads to unwanted mixing between operators of different chiral sectors, exceptional configurations when the simulated quark masses approach their physical values, and no clear definition of a topological index. The overlap Dirac operator solves these problems by satisfying a lattice variant of chiral symmetry, meaning that among the various lattice formulations used today, it is closest to the continuum Dirac operator. In particular, it has a well defined topological index which correctly accounts for the U(1) anomaly. This makes overlap fermions the obvious choice when it comes to simulations focusing on topological properties of the vacuum of QCD, on observables sensitive to chiral symmetry breaking or phenomenology close to the physical quark masses. However, using overlap fermions in practise is particularly challenging for two reasons: Firstly, they require a large amount of computer resources. The overlap Dirac operator contains the sign function of a large sparse matrix. As a consequence, inversions of the operator, required in any Hybrid Monte Carlo (HMC) algorithm or calculation of an observable, involve a two-level nested inversion. We have introduced new inversion algorithms accelerating this inversion by a factor of 10 [1]. Secondly, a HMC algorithm requires the differential of the sign function, leading to a delta function in the fermionic force. By treating small eigenvalues of the sparse matrix exactly and employing a reflection/transmission algorithm we have constructed a HMC algorithm which has