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 5-th dimension is introduced such that massless quarks with exact chiral symmetry can be realized at finite lattice spacing, on the boundaries of the 5-th dimension, the so-called domain-wall fermion (DWF). In this talk, I discuss how to simulate lattice QCD with DWF such that the chiral symmetry can be preserved optimally with a finite extent in the 5-th dimension. I also outline the simulations which have been performing by the TWQCD Collaboration and present some recent physical results.