Hannes Vogt

Coulomb, Landau and maximally Abelian gauge fixing in lattice QCD with multi-GPUs

Abstract A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA’s CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single- (SP) and double-precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed-precision scheme that performs the critical parts of the algorithm in full DP while retaining 80%–90% of the SP performance. Finally, multi-GPUs are adopted to overcome the memory constraint of single GPUs. A communicator class which hides the MPI data exchange at the boundaries of the lattice domains, via the low bandwidth PCI-Bus, effectively behind calculations in the inner part of the domain is presented. Linear scaling using 16 NVIDIA Tesla C2070 devices and a maximum performance of 3.5 Teraflops on lattices of size down to 64 3 × 256 is demonstrated.

Coulomb versus physical string tension on the lattice

From continuum studies it is known that the Coulomb string tension

Gauge fixing using overrelaxation and simulated annealing on GPUs

{\ensuremath{\sigma}}_{C}

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

gives an upper bound for the physical (Wilson) string tension

Gribov horizon and Gribov copies effect in lattice Coulomb gauge

{\ensuremath{\sigma}}_{W}

Coulomb gauge on the lattice: From zero to finite temperature

[D. Zwanziger, Phys. Rev. Lett. 90, 102001 (2003)]. How does such a relationship translate to the lattice, however? In this paper we give evidence that on the lattice, while the two string tensions are related at zero temperature, they decouple at finite temperature. More precisely, we show that on the lattice the Coulomb gauge confinement scenario is always tied to the spatial string tension, which is known to survive the deconfinement phase transition and to cause screening effects in the quark-gluon plasma. Our analysis is based on the identification and elimination of center vortices, which allows us to control the physical string tension and study its effect on the Coulomb gauge observables. We also show how alternative definitions of the Coulomb potential may sense the deconfinement transition; however, a true static Coulomb gauge order parameter for the phase transition is still elusive on the lattice.

Lattice QCD Green’s functions in maximally Abelian gauge: Infrared Abelian dominance and the quark sector

We adopt CUDA-capable Graphic Processing Units (GPUs) for Coulomb, Landau and maximally Abelian gauge fixing in 3+1 dimensional SU(3) lattice g auge field theories. The local overrelaxation algorithm is perfectly suited for highly pa rallel architectures. Simulated annealing preconditioning strongly increases the probability to reach the global maximum of the gauge functional. We give performance results for single and double precision. To obtain our maximum performance of 300 GFlops on NVIDIA’s GTX 580 a very fine grain ed degree of parallelism is required due to the register limits of NVIDIA’s Fermi GPUs: w e use eight threads per lattice site, i.e., one thread per SU(3) matrix that is involved in the computation of a site update.

Confinement in Coulomb gauge

We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang–Mills theory, the deconfinement phase transition is found to be second order for and first order for , in agreement with the lattice results. The corresponding critical temperatures are found to be and , respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of and , respectively, for the deconfinement and chiral transition.

Gauge fixing in lattice QCD with multi-GPUs

Following a recent proposal by Cooper and Zwanziger we investigate via

Hamiltonian approach to QCD in Coulomb gauge: Gribov’s confinement scenario at work

SU(2)