## Visualization of Lattice Gauge QCD Simulations at NERSC

The following technical information was copied from
Greg Kilcup's Lattice Gauge Theory web page at Ohio State University:

This is a visualization of some of the first data to come off the new
128-node Cray T3E recently installed at NERSC (circa 1997). The still
frames below show
part of an eigenmode of the Dirac operator. Since we work in four dimensions
the full structure cannot be shown in one picture; these images show single
three dimensional slices. If your browser is Java-capable, click on one of
the images below to animate the frames and see the full four-dimensional
object as we loop over the supressed dimension.

Lattice QCD is the subfield of particle theory which attempts to solve QCD
problems by approximating spacetime with a discrete grid. Once they are put
on a grid, these problems can be attacked by a variety of means, most often
involving numerical methods on (super-)computers. The approach was invented
by OSU's own Ken Wilson in 1974, and has since evolved in to major discipline
within particle physics. The OSU group is currently involved with several
large-scale numerical simulations aimed at understanding strong and weak
interaction properties of heavy and light quarks. Among these is the
collaboration which has recently (Feb 1997) been named one of the
Department of Energy Grand Challenges.

We use the simple Wilson plaquette action on a 32*32*32*64 lattice, with
beta=6.4, and staggered quarks. The boundaries are periodic in each of
the four dimensions. The configuration was cooled slightly (20 steps) to
erase short-distance fluctuations. We used inverse iteration to converge
to the eigenvector with the smallest eigenvalue. More precisely, we have
isolated an eigenvector of Dslash-squared. It is a linear combination of
the pair of related lowest eigenvectors of Dslash (with eigenvalues
lambda and -lambda). The fact that the eigenmode is localized is
interesting. (Higher modes would look like uniform uninteresting
planewaves.) Though we have not yet checked explicitly, we expect that
the eigenmode is "pinned" on top of instantons, topologically nontrivial
knots in the underlying gauge field. These localized modes are a special
feature of non-Abelian gauge theories, and are part of what makes QCD so
hard to solve. Ultimately, the size and shape of such eigenmodes is
believed to be responsible for basic properties of matter, such as the
the size and mass of the proton.