RSS Feed MONTE CARLO SIMULATIONS OF QCD
Doug Toussaint and Robert Sugar
Scientific Significance:
The MILC (MIMD Lattice Computations) collaboration has been using the T3D at PSC to study the high temperature behavior of quantum chromdynamics, the theory of the strong interaction. At a temperature of around 150 Mev, or 1012 Kelvins, the quarks and gluons which are tightly bound into hadrons at ordinary temperatures become free to move about over much longer distances, creating the so-called "quark-gluon plasma." The properties of the high temperature phase and of the transition or crossover to this phase are important for understanding the evolution of the early universe and for the interpretation of experiments at the Relativistic Heavy Ion Collider (RHIC) now under construction at Brookhaven.
Numerical simulation of lattice QCD is the only known technique for studying this problem for which all the approximations are systematically improvable. This systematic improvement involves simulating the system on larger physical lattices, with smaller lattice spacings, with more realistic quark masses, and with better statistics. All of these improvements require large computing power. The problem is a natural one for parallel machines since similar computations must be done at each site of a four dimensional space-time lattice, and the lattice sites are simply divided among the processors.
The actual computations require generation of a set of sample field configurations, where the field is defined on a four dimensional grid. Generating these configurations requires integrating equations of motion, and the force computation at each step requires solution of a large (500,000 by 500,000 in our case) sparse matrix problem. The conjugate gradient algorithm used for "inverting" the sparse matrix uses the bulk of our cpu time. Once the samples are generating, physical observables are estimated by averaging over these configurations.
In our current project, we are exploring high temperature QCD with a lattice spacing 2/3 as large as the best previous calculations. It is particularly important to reduce the lattice spacing, since the full chiral symmetry which is thought to control the phase transition is restored only in the limit of zero lattice spacing. Thus the temperature and even the order of the phase transition could be affected by a too-large lattice spacing. Unfortunately, decreasing the lattice spacing by a factor of 2/3 increases the number of points in the four dimensional lattice, and thus the work involved, by a factor of 3/2 to the fourth power, or about five. Simply determining the approximate transition temperature and the simplest properties of the crossover region at this lattice spacing requires hundreds of thousands of node-hours, so this project could not be done without large amounts of time on parallel machines of the T3D class. By combining runs made on the PSC T3D with runs made on the CM5 and Paragon, we expect to present preliminary results on the high temperature crossover at this lattice spacing at the Lattice-94 conference in Bielefeld, Germany in September.
Numerical Approach and Performance:
Our group has developed a portable QCD code for MIMD machines, in which all the machine dependent communication routines are isolated in a single file with a different version of this file for each machine. Thus all the high level code (95 percent of the code) is common to all the machines. The code currently runs on scalar machines, the Intel Paragon, the Ncube-2, the IBM SP-1, the Thinking Machines CM5 and the Cray T3D.
To benchmark this code, we measure the speed of the conjugate gradient routine used in computing the quarks' contribution to the force in the molecular dynamics integration, since this takes up over 90 percent of the computing time. In these benchmarks, the lattice size is 4096 sites per node. Both the Intel Paragon and T3D code include some low level hand-coded assembler language routines, while the CM5 code includes a CDPEAC conjugate gradient routine written by Charlie Liu. The numbers quoted are megaflops per node.
NODES Paragon CM5 T3D 1 27.1 NA 26.9 16 23.6 NA 22.1 64 23.2 20 22.2
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