Recent Progress in Lattice QCD

2008

In this study, we focus on assessing the efficiency and the performance expected for the Lattice QCD problem on representative architectures and we project the expected improvement on these architectures and their impact on performance for Lattice QCD. We additionally try to pinpoint the limiting factors for performance on these architectures.

Nuclear physics, 1997

We study a coupling flow of pure QCD gauge system by using the Monte Carlo Renormalization Group method. A rough location of the renormalized trajectory in two coupling space is obtained. Also we compare 4 different actions; (a)standard Wilson, (b)Symanzik's, (c)Iwasaki's and (d)QCDTARO's. The rotational symmetry is restored better as an action gets close to the renormalized trajectory.

1998

The enormous computing resources that large-scale simulations in Lattice QCD require will continue to test the limits of even the largest supercomputers into the foreseeable future. The efficiency of such simulations will therefore concern practitioners of lattice QCD for some time to come. I begin with an introduction to those aspects of lattice QCD essential to the remainder of the thesis, and follow with a description of the Wilson fermion matrix M, an object which is central to my theme. The principal bottleneck in Lattice QCD simulations is the solution of linear systems involving M, and this topic is treated in depth. I compare some of the more popular iterative methods, including Minimal Residual, Corij ugate Gradient on the Normal Equation, BI-Conjugate Gradient, QMR., BiCGSTAB and BiCGSTAB2, and then turn to a study of block algorithms, a special class of iterative solvers for systems with multiple right-hand sides. Included in this study are two block algorithms which had ...

Nuclear Physics B- …, 1997

We describe a number of aspects in our attempt to construct an approximately perfect lattice action for QCD. Free quarks are made optimally local on the whole renormalized trajectory and their couplings are then truncated by imposing 3-periodicity. The spectra of these short ranged fermions are excellent approximations to continuum spectra. The same is true for free gluons. We evaluate the corresponding perfect quark-gluon vertex function, identifying in particular the \perfect clover term". First simulations for heavy quarks show that the mass is strongly renormalized, but again the renormalized theory agrees very well with continuum physics. Furthermore we describe the multigrid formulation for the non-perturbative perfect action and we present the concept of an exactly (quantum) perfect topological charge on the lattice.

Nuclear Physics B, 1990

A method proposed by Barbour, Davies and Sabeur is used to expand the grand canonical partition function for QCD on a finite lattice in terms of the canonical partition functions for a fixed number of fermions. We show how the lattice action corresponding to the canonical partition function for a given fermion number can be obtained. The method is not unique to QCD and can be applied to other theories with complex action. This expansion of the GCPF is used to study QCD at finite density. The results of preliminary numerical simulations performed on a 44 lattice are described. Evidence is found for the positivity and continuity of the canonical partition functions as a function of the fermion number. The number density shows a clear signal of a transition at a density (in lattice units) of about 0.35 at /3 = 4.9 and small quark mass.

Journal of High …, 2006

Journal of Physics: Conference Series, 2006

I present our recent results on the critical end point in the µ B -T phase diagram of QCD with two flavours of light dynamical quarks and compare them with similar results from other groups. Implications for a possible energy scan at the RHIC are discussed. I also comment briefly on the new results of great relevance to heavy ion collisions from finite temperature lattice QCD simulations on speed of sound, specific heat and on the fate of J/ψ.

2017

To observe the phenomenon of quark confinement it is needed to investigate whether the linear term in QCD potential actually exists. For this purpose perturbative techniques were insufficient. But numerical simulations of lattice gauge theory on a space time lattice is an important tool for lattice QCD calculations. In this paper we review the Wilson loop techniques for the study of quark confinement using the gauge invariance.

We pursue the idea of adding the naive $\mu N$ term, where $\mu$ is the quark chemical potential and $N$ is the conserved quark number, to the lattice QCD action. While computations of higher order susceptibilities, required for estimating the location of the QCD critical point, need a lot fewer number of quark propagators at any order as a result, it has its problem. We discuss a solution, and examine if it works.

Physical Review D, 1998