## Group QCD

Group Description Quantum Chromodynamics, B. Medeke, Univ. Wuppertal, Germany Source: Bjoern Medeke, Department of Mathematics, Institute of Applied Computer Science, University of Wuppertal, 42097 Wuppertal, Germany. Phone: +49 202 439-3776. Email: medeke at math.uni-wuppertal.de Discipline: Physics Accession (in Matrix Market collection): 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 \gamma_5 = \left( \begin{array}{cccc} 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{array}\right) the Wilson fermion matrix A is Gamma-5 symmetric, \Gamma_5 A = A^H \Gamma_5,\;\;\;\;\Gamma_5 = I \otimes ( \gamma_5 \otimes I_3 ) 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 D = \left( \begin{array}{cc} 0 & D_{\rm oe} \\D_{\rm eo} & 0 \end{array}\right) 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.
Displaying all 14 collection matrices
Id Name Group Rows Cols Nonzeros
1591 conf5_0-4x4-10 QCD 3,072 3,072 119,808
1592 conf5_0-4x4-14 QCD 3,072 3,072 119,808
1593 conf5_0-4x4-18 QCD 3,072 3,072 119,808
1594 conf5_0-4x4-22 QCD 3,072 3,072 119,808
1595 conf5_0-4x4-26 QCD 3,072 3,072 119,808
1598 conf5_4-8x8-05 QCD 49,152 49,152 1,916,928
1599 conf5_4-8x8-10 QCD 49,152 49,152 1,916,928
1600 conf5_4-8x8-15 QCD 49,152 49,152 1,916,928
1601 conf5_4-8x8-20 QCD 49,152 49,152 1,916,928
1596 conf6_0-4x4-20 QCD 3,072 3,072 119,808
1597 conf6_0-4x4-30 QCD 3,072 3,072 119,808
1602 conf6_0-8x8-20 QCD 49,152 49,152 1,916,928
1603 conf6_0-8x8-30 QCD 49,152 49,152 1,916,928
1604 conf6_0-8x8-80 QCD 49,152 49,152 1,916,928