格點量子色動力學之數值研究

Abstract

量子色動力學(QCD)為夸克(quark)與膠子(gluon)相互作用的基礎理論。其在原子核內顯示為短距強交互作用力，並在早期宇宙之演進-由夸克膠子漿相至強子相中扮演了重要角色。闡述量子色動力學是個巨大挑戰，因為這需要在四維離散時空上對量子色動力學作用量(action)進行極大尺度之的數值模擬。此外，由於夸克在相對論表述下為費米子(fermion)，在無質量時具有精確手則對稱。因此，需要引入第五維度使無質量之夸克在第五維度的邊界實現，並在有限晶格間距下具有精確手則對稱，稱為domain-wall夸克。因為顯示卡(GPU)在高速運算中成為了強有力的工具，我們探討如何使用多顯示卡來模擬格點量子色動力學。我們討論如何使用多顯示卡去模擬極大尺度domain-wall夸克之策略，並且概述其演算法，以及去如何實施在顯示卡上。我們展示了程式的運算基準（benchmarks），並呈現hybrid Monte Carlo (HMC)模擬的特徵結果。

Quantum chromodynamics (QCD) is the fundamental theory for the interaction between quarks and gluons. It manifests as the short-range strong interaction inside the nucleus and plays an important role in the evolution of the early universe, from the quark-gluon plasma phase to the hadron phase. To solve QCD is a grand challenge, since it requires very large-scale numerical simulations of the discretized action of QCD on the 4-dimensional space-time lattice. Moreover, since quarks are relativistic fermions, the fifth dimension is introduced such that massless quarks with exact chiral symmetry can be realized at finite lattice spacing, on the boundaries of the fifth dimension, the so-called domain-wall fermion (DWF). Since the GPU (graphic processing unit) has become the most powerful device in supercomputing, we aim at developing optimized codes for the simulation of lattice QCD with multi-GPUs. In this thesis, we discuss our strategy how to use multi-GPUs to tackle the very large-scale simulation of lattice QCD with DWF, and outline our computational algorithm and its implementation for multi-GPUs. We perform the benchmarks of our code, and present the characteristics of our hybrid Monte Carlo (HMC) simulations for various lattice sizes.