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Register a new userThe Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices
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The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $ beta_E $, in obtaining these results.
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We present results for the equation of state for pure SU(3) gauge theory obtained on anisotropic lattices with the anisotropy $xi equiv a_s/a_t = 2$. The pressure and energy density are calculated on $N_t / xi = 4, 5$ and 6 lattices with the integral method. They are found to satisfy the leading $1/N_t^2$ scaling from our coarsest lattice $N_t/xi=4$. This enables us to carry out well controlled continuum extrapolations. We find that the pressure and energy density agree with those obtained using the isotropic plaquette action, but have smaller and more reliable errors.
A `forward walking Greens Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.
As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Here, we adopt the highly-improved staggered quark action with the tree-level Symanzik gauge action (HISQ/tree), which is exactly the same as the setup for our simulations for $SU(3)$ gauge theories with $N_f=8$, $12$ and $16$ fundamental fermions~cite{Aoki:2013xza, Aoki:2012eq, Aoki:2014oma}. In the next section, we show the fermion mass dependence of $F_pi$, $langlebar{psi}psirangle$, $M_pi$, $M_rho$, $M_N$ and their chiral extrapolations. In section 3, preliminary results of the measurement of the mass of the flavor-singlet scalar bound state will be reported.
We study thermodynamics of SU(3) gauge theory at fixed scales on the lattice, where we vary temperature by changing the temporal lattice size N_t=(Ta_t)^{-1}. In the fixed scale approach, finite temperature simulations are performed on common lattice spacings and spatial volumes. Consequently, we can isolate thermal effects in observables from other uncertainties, such as lattice artifact, renormalization factor, and spatial volume effect. Furthermore, in the EOS calculations, the fixed scale approach is able to reduce computational costs for zero temperature subtraction and parameter search to find lines of constant physics, which are demanding in full QCD simulations. As a test of the approach, we study the thermodynamics of the SU(3) gauge theory on isotropic and anisotropic lattices. In addition to the equation of state, we calculate the critical temperature and the static quark free energy at a fixed scale.
We systematically compare filtering methods used to extract topological excitations from lattice gauge configurations. We show that there is a strong correlation of the topological charge densities obtained by APE and Stout smearing. Furthermore, a first quantitative analysis of quenched and dynamical configurations reveals a crucial difference of their topological structure: the topological charge density is more fragmented, when dynamical quarks are present. This fact also implies that smearing has to be handled with great care, not to destroy these characteristic structures.
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