Simulating maximally twisted fermions at the physical pointa with multigrid methods

Abstract

We develop multigrid methods for simulating lattice QCD with physical values of the quark masses within the twisted mass fermion formulation. We employ the developed multigrid method both for the calculation of the quark propagators needed for extracting the hadronic matrix elements and for accelerating the generation of gauge field ensembles. For the computation of the quark propagators we improve the performance by two orders of magnitudes as compared to conjugate gradient enabling to perform the analysis of key nucleon observables at physical values of the light quark mass. For the generation of gauge field ensembles with two degenerate flavors of the light quarks (Nf =2) an order of magnitude speedup is achieved. Extension of the multigrid approach is carried out to include in the simulation the dynamical strange and charm quarks. To accomplish this one needs the calculation of the square root of the non-degenerate twisted mass operator. We solve the square root with an optimal rational approximation and employ multigrid methods in the solution of the shifted linear system. In such a way we accelerate simulations with Nf =2+1+1 flavors of fermions all tuned at their physical value by an order of one magnitude. These methods are used for the production of four ensembles, two with Nf =2 and two with Nf =2+1+1, which are state-of-the-art worldwide. These ensembles are shared by all members of the Extended Twisted Mass Collaboration (ETMC) and are being used them for obtaining quantitative description of hadron properties including observables that can probe new physics beyond the standard model. In this thesis we focus on physical results on low-lying hadron masses, meson decay constants, and pion and nucleon electromagnetic form factors