Simulation of quantum chromodynamics on the lattice with exactly chiral lattice fermions

摘要

Numerical simulation of the low-energy dynamics of quarks and gluons is now feasible based on the fundamental theory of strong interaction, i.e. quantum chromodynamics (QCD). With QCD formulated on a 4D hypercubic lattice (called lattice QCD or LQCD), one can simulate the QCD vacuum and hadronic excitations on the vacuum using teraflop-scale supercomputers, which have become available in the last decade. A great deal of work has been done on this subject by many groups around the world; in this article we summarize the work done by the JLQCD and TWQCD collaborations since 2006. These collaborations employ Neuberger's overlap fermion formulation, which preserves the exact chiral and flavor symmetries on the lattice, unlike other lattice fermion formulations. Because of this beautiful property, numerical simulation of the formulation can address fundamental questions on the QCD vacuum, such as the microscopic structure of the quark–antiquark condensate in the chirally broken phase of QCD and its relation to SU(3) gauge field topology. Tests of the chiral effective theory, which is based on the assumption that the chiral symmetry is spontaneously broken in the QCD vacuum, can be performed, including the pion-loop effect test. For many other phenomenological applications, we adopt the all-to-all quark propagator technique, which allows us to compute various correlation functions without substantial extra cost. The benefit of this is not only that the statistical signal is improved but that disconnected quark-loop diagrams can be calculated. Using this method combined with the overlap fermion formulation, we study a wide range of physical quantities that are of both theoretical and phenomenological interest.