Simulation of lattice QCD with domain-wall fermions

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 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 so 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). In this work, I discuss how to simulate lattice QCD with DWF so that the chiral symmetry can be preserved optimally with a finite extent in the fifth dimension. I also outline the simulations which have been performed by the TWQCD Collaboration and present some recent physical results.