The QPACE Supercomputer Applications of Random Matrix Theory in Two-Colour Quantum Chromodynamics Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der Fakult¨atf¨urPhysik der Universit¨atRegensburg vorgelegt von Nils Meyer aus Kempten im Allg¨au Mai 2013 Die Arbeit wurde angeleitet von: Prof. Dr. T. Wettig Das Promotionsgesuch wurde eingereicht am: 07.05.2013 Datum des Promotionskolloquiums: 14.06.2016 Pr¨ufungsausschuss: Vorsitzender: Prof. Dr. C. Strunk Erstgutachter: Prof. Dr. T. Wettig Zweitgutachter: Prof. Dr. G. Bali weiterer Pr¨ufer: Prof. Dr. F. Evers F¨urDenise. Contents List of Figures v List of Tables vii List of Acronyms ix Outline xiii I The QPACE Supercomputer 1 1 Introduction 3 1.1 Supercomputers . .3 1.2 Contributions to QPACE . .5 2 Design Overview 7 2.1 Architecture . .7 2.2 Node-card . .9 2.3 Cooling . 10 2.4 Communication networks . 10 2.4.1 Torus network . 10 2.4.1.1 Characteristics . 10 2.4.1.2 Communication concept . 11 2.4.1.3 Partitioning . 12 2.4.2 Ethernet network . 13 2.4.3 Global signals network . 13 2.5 System setup . 14 2.5.1 Front-end system . 14 2.5.2 Ethernet networks . 14 2.6 Other system components . 15 2.6.1 Root-card . 15 2.6.2 Superroot-card . 17 i ii CONTENTS 3 The IBM Cell Broadband Engine 19 3.1 The Cell Broadband Engine and the supercomputer league . 19 3.2 PowerXCell 8i overview . 19 3.3 Lattice QCD on the Cell BE . 20 3.3.1 Performance model . 21 3.3.2 Lattice QCD kernel . 22 3.3.3 Data layout analysis . 22 3.4 DMA transaction models . 24 3.4.1 Local Store to Local Store . 25 3.4.2 Local Store to main memory . 26 4 The QPACE Network Processor 29 4.1 FPGA technology . 29 4.2 Network processor overview . 30 4.3 Device Control Register bus . 32 4.3.1 Device tree topology . 33 4.3.2 Bus interface and protocol . 34 4.3.3 Master implementation . 36 4.3.4 Arbiter implementation . 37 4.3.5 Synchronous DCR interface implementation . 39 4.4 Inbound Write Controller . 41 4.4.1 Implementation . 43 4.4.2 State machine . 46 4.5 Universal Asynchronous Receiver Transmitter . 47 4.5.1 Implementation . 48 4.5.2 Register file and modes of operation . 50 5 System Verification and Software Tools 53 5.1 System tests . 53 5.2 Software tests . 54 5.3 Booting the node-cards: ncBoot ............................. 55 5.3.1 Implementation . 55 5.3.2 Command line interface . 56 5.3.3 State machine . 57 5.4 QPACE Front-end Client . 57 5.4.1 Implementation . 58 5.4.2 Command line interface . 59 5.4.3 Error handling . 60 CONTENTS iii II Applications of Random Matrix Theory in Two-Colour Quantum Chro- modynamics 63 6 Quantum Chromodynamics 65 6.1 Introduction . 65 6.2 Non-Abelian gauge theory . 66 6.3 Chiral symmetry . 68 6.3.1 Introduction . 68 6.3.2 Gauge group SU(3) . 69 6.3.3 Gauge group SU(2) . 69 6.3.4 Chiral condensate . 70 6.4 Low-energy effective theory . 71 6.4.1 Motivation . 71 6.4.2 Lagrangian of the effective theory . 72 6.4.3 Non-zero baryon chemical potential . 73 6.5 Lattice QCD . 74 6.6 Fermions on the lattice . 76 6.6.1 Wilson-Dirac operator . 76 6.6.2 Lattice chiral symmetry . 78 6.6.3 Overlap operator . 81 6.7 Chemical potential on the lattice . 82 7 Random Matrix Theory 85 7.1 Introduction . 85 7.2 Hermitian chiral random matrix theory . 86 7.3 Non-Hermitian chiral random matrix theory . 89 8 Evaluation and Results 95 8.1 Two-colour QCD at zero chemical potential . 95 8.1.1 Choice of the Wilson mass . 95 8.1.2 Analysis of the distribution of the lowest-lying eigenvalue . 98 8.1.3 Analysis of the spectral density . 99 8.2 Two-colour QCD at non-zero chemical potential . 107 8.2.1 Spectrum of the overlap operator . 107 8.2.2 Analysis of the spectral density . 109 9 Summary 117 9.1 QPACE ........................................... 117 9.2 Lattice simulations of two-colour QCD . 117 iv CONTENTS Appendix 119 A QPACE Addendum 119 A.1 Sources . 119 A.2 DCR memory map . 120 A.3 witchlib API . 122 A.4 QFC full reference . 124 A.4.1 PSU specific actions . 124 A.4.2 Node-card specific actions . 125 A.4.2.1 Get mode . 125 A.4.2.2 Set mode . 126 A.4.2.3 Power mode . 126 A.4.2.4 Clear mode . 127 A.4.2.5 Flash mode . 128 B Numerical Simulation 129 B.1 Krylov-Ritz method . 129 B.2 Statistical bootstrap . 132 References 135 List of Publications 143 Danksagung 145 List of Figures 2.1 QPACE functional units . .8 2.2 QPACE at JSC . ..