## QCD: Quantum Chromodynamics

### from the Independent Sets and Generators

Set QCD
Source: Bjoern Medeke, Department of Mathematics, Institute of Applied Computer Science, University of Wuppertal, 42097 Wuppertal, Germany. Phone: +49 202 439-3776. Email: medeke@math.uni-wuppertal.de
Discipline: Physics
Accession: December 2000

Background. Lattice gauge theory is a discretization of quantum chromodynamics which is generally accepted to be the fundamental physical theory of strong interactions among the quarks as constituents of matter. The most time-consuming part of a numerical simulation in lattice gauge theory with Wilson fermions on the lattice is the computation of quark propagators within a chromodynamic background gauge field. These computations use up a major part of the world's high performance computing power.

Quark propagators are obtained by solving the inhomogeneous lattice Dirac equation Ax = b, where A = I - kD with 0 <= k < kc is a large but sparse complex non-Hermitian matrix representing a periodic nearest-neighbour coupling on a four-dimensional Euclidean space-time lattice.

From the physical theory it is clear that the matrix A should be positive real (all eigenvalues lie in the right half plane) for 0 <= k < kc. Here, kc represents a critical parameter which depends on the given matrix D. Denoting

the Wilson fermion matrix A is Gamma-5 symmetric,

Due to the nearest neighbour coupling, the matrix A has 'property A'. This means that with a red-black (or odd-even) ordering of the grid points the matrix becomes

A = I - kD
with

Set of QCD Matrices. The QCD matrices provided in the set QCD consist of realistic matrices D generated at different physical temperatures b.

 matrix D b order nonzeros kc conf5.0-00l4x4-1000.mtx 5.0 3072 119808 0.20611 conf5.0-00l4x4-1400.mtx 5.0 3072 119808 0.20328 conf5.0-00l4x4-1800.mtx 5.0 3072 119808 0.20265 conf5.0-00l4x4-2200.mtx 5.0 3072 119808 0.20235 conf5.0-00l4x4-2600.mtx 5.0 3072 119808 0.21070 conf6.0-00l4x4-2000.mtx 6.0 3072 119808 0.15968 conf6.0-00l4x4-3000.mtx 6.0 3072 119808 0.16453 conf5.4-00l8x8-0500.mtx 5.4 49152 1916928 0.17865 conf5.4-00l8x8-1000.mtx 5.4 49152 1916928 0.17843 conf5.4-00l8x8-1500.mtx 5.4 49152 1916928 0.17689 conf5.4-00l8x8-2000.mtx 5.4 49152 1916928 0.17835 conf6.0-00l8x8-2000.mtx 6.0 49152 1916928 0.15717 conf6.0-00l8x8-3000.mtx 6.0 49152 1916928 0.15649 conf6.0-00l8x8-8000.mtx 6.0 49152 1916928 0.15623

References. A survey of lattice gauge theory is given in

1. M. Creutz: Quarks, Gluons, and Lattices, Cambridge University Press, (1986)
2. I. Montvay and G. Munster: Quantum Fields on the Lattice, Cambridge University Press (1994)
More background information can be found at various locations on the Web. Search for "High Energy Physics" (HEP). A list of HEP Web sites is available at CERN (European Laboratory for Particle Physics).

A PostScript version of this information is also available.

## Matrices in this set:

• conf5.0-00l4x4-1000 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=5.0, kc=0.20611
• conf5.0-00l4x4-1400 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=5.0, kc=0.20328
• conf5.0-00l4x4-1800 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=5.0, kc=0.20265
• conf5.0-00l4x4-2200 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=5.0, kc=0.20235
• conf5.0-00l4x4-2600 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=5.0, kc=0.21070
• conf6.0-00l4x4-2000 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=6.0, kc=0.15968
• conf6.0-00l4x4-3000 (complex unsymmetric, 3072 by 3072, 119808 entries), Quantum chromodynamics, b=6.0, kc=0.16453
• conf5.4-00l8x8-0500 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=5.4, kc=0.17865
• conf5.4-00l8x8-1000 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=5.4, kc=0.17843
• conf5.4-00l8x8-1500 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=5.4, kc=0.17689
• conf5.4-00l8x8-2000 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=5.4, kc=0.17835
• conf6.0-00l8x8-2000 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=6.0, kc=0.15717
• conf6.0-00l8x8-3000 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=6.0, kc=0.15649
• conf6.0-00l8x8-8000 (complex unsymmetric, 49152 by 49152, 1916928 entries), Quantum chromodynamics, b=6.0, kc=0.15623

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