Abstract:
I derive the equation of motion in molecular dynamics for doing full lattice QCD simulations with clover quarks. The even-odd preconditioning technique, expected to significantly reduce the computational effort, is further developed for the simulations.

Abstract:
First principle study of QCD at finite temperature $T$ and chemical potential $\mu$ is essential for understanding a wide range of phenomena from heavy-ion collisions to cosmology and neutron stars. However, in the presence of finite density, the critical behavior lattice gauge theory without species doubling, is unknown. At strong coupling, we examine the phase structure on the $(\mu,T)$ plane, using Hamiltonian lattice QCD with Wilson fermions. A tricritical point is found, separating the first and second order chiral phase transitions. Such a tricritical point at finite $T$ has not been found in previous work in the Hamiltonian formalism with Kogut-Susskind fermions or naive fermions.

Abstract:
We review the recent glueball mass calculations using an efficient method for solving the Schr\"odinger equation order by order with a scheme preserving the continuum limit. The reliability of the method is further supported by new accurate results for (1+1)-dimensional $\sigma$ models and (2+1)-dimensional non-abelian models. We present first and encouraging data for the glueball masses in 3+1 dimensional QCD.

Abstract:
I describe a mechanism to understand the relation between chiral-symmetry breaking and eigenmodes of the Dirac operator in lattice QCD with Kogut-Susskind sea quarks. It can be shown that if chiral symmetry is spontaneously broken, the eigenvalues $\lambda_i$ should behave as $z(i)/V$ for large volume $V$, where $z(i)$ is the i-th zero of the Bessel function. With neither chiral nor $\lambda$ extrapolation, one can precisely calculate the chiral condensate using only a small set of eigenvalues. Therefore, it is economical and free of systematic uncertainties. I present the first QCD data to support this mechanism and encourage the lattice community to test and use it.

Abstract:
One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods, one has to perform expensive lattice simulations at multiple bare quark masses, and employ some modeled function to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicates that the method might be a more efficient alternative for investigating the spontaneous chiral-symmetry breaking in lattice QCD.

Abstract:
The vacuum properties of lattice QCD with staggered quarks are investigated by an efficient simulation method. I present data for the quark condensate with flavor number $N_f=0, ~ 1, ~ 2, ~ 3, ~ 4$ and many quark masses, including the vacuum energy in the chiral limit. Obvious sea quark effects are observed in some parameter space. I also describe a mechanism to understand this and a formula relating the chiral condensate and zero modes.

Abstract:
I extend to QCD an efficient method for lattice gauge theory with dynamical fermions. Once the eigenvalues of the Dirac operator and the density of states of pure gluonic configurations at a set of plaquette energies (proportional to the gauge action) are computed, thermodynamical quantities deriving from the partition function can be obtained for arbitrary flavor number, quark masses and wide range of coupling constants, without additional computational cost. Results for the chiral condensate and gauge action are presented on the $10^4$ lattice at flavor number $N_f=0$, 1, 2, 3, 4 and many quark masses and coupling constants. New results in the chiral limit for the gauge action and its correlation with the chiral condensate, which are useful for analyzing the QCD chiral phase structure, are also provided.

Abstract:
In a recent funded Key Project of National Science Foundation of China, we have planned to do large scale simulations of lattice Quantum Chromodynamics, using the parallel supercomputing facilities in mainland China. Here I briefly review our plan and progress in recent years.

Abstract:
We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for SU(3) gauge theory with quenched Kogut-Susskind quarks on the $10^4$ lattice are shown.

Abstract:
The ground and first excited states of the hybrid charmonium ${\bar c} c g$, with non-exotic quantum numbers $J^{PC}=0^{-+}$, $1^{--}$ and $1^{++}$ are investigated using quenched lattice QCD. They are completely ignored in the literature, only because their ground states are degenerate with $\eta_c$, $J/\psi$, and $\chi_{c1}$, and are difficult to be distinguished from these conventional charmonium mesons in experiment. However, we observe strong gluonic radial excitations in the first excited states; We predict that their masses are 4.352(225)GeV, 4.379(149)GeV and 7.315(257)GeV, completely different from the first excited states of the corresponding conventional charmonium. Their relevance to the recent discovery of the Y(4260) state and future experimental search for other states are also discussed.