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Register a new userParallel implementation of a lattice-gauge-theory code: studying quark confinement on PC clusters
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Added by
Attilio Cucchieri
Publication date
2003
fields
Informatics Engineering
and research's language is
English
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We consider the implementation of a parallel Monte Carlo code for high-performance simulations on PC clusters with MPI. We carry out tests of speedup and efficiency. The code is used for numerical simulations of pure SU(2) lattice gauge theory at very large lattice volumes, in order to study the infrared behavior of gluon and ghost propagators. This problem is directly related to the confinement of quarks and gluons in the physics of strong interactions.
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We calculate the lattice quark propagator in Coulomb gauge both from dynamical and quenched configurations. We show that in the continuum limit both the static and full quark propagator are multiplicatively renormalizable. From the propagator we extract the quark renormalization function Z(|p|) and the running mass M(|p|) and extrapolate the latter to the chiral limit. We find that M(|p|) practically coincides with the corresponding Landau gauge function for small momenta. The computation of M(|p|) can be however made more efficient in Coulomb gauge; this can lead to a better determination of the chiral mass and the quark anomalous dimension. Moreover from the structure of the full propagator we can read off an expression for the dispersion relation of quarks, compatible with an IR divergent effective energy. If confirmed on larger volumes this finding would allow to extend the Gribov-Zwanziger confinement mechanism to the fermionic sector of QCD.
We study quark confinement physics using lattice QCD. In the maximally abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large effective off-diagonal gluon mass, M_off=1.2GeV. Due to the large off-diagonal gluon mass in the MA gauge, low-energy QCD is abelianized like nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network of the monopole world-line covering the whole system. We extract and analyze the dual gluon field B_mu from the monopole-current system in the MA gauge, and evaluate the dual gluon mass as m_B = 0.4-0.5GeV in the infrared region, which is a lattice-QCD evidence of the dual Higgs mechanism by monopole condensation. Even without explicit use of gauge fixing, we can define the maximal abelian projection by introducing a ``gluonic Higgs field phi(x), whose hedgehog singularities lead to monopoles. From infrared abelian dominance and infrared monopole condensation, infrared QCD is describable with the dual Ginzburg-Landau theory. In relation to the color-flux-tube picture for baryons, we study the three-quark (3Q) ground-state potential V_3Q in SU(3) lattice QCD at the quenched level, with the smearing technique for enhancement of the ground-state component. With accuracy better than a few %, V_3Q is well described by a sum of the two-body Coulomb part and the three-body linear confinement part sigma_3Q L_min, where L_min denotes the minimal value of the total length of the color flux tube linking the three quarks. Comparing with the Q-barQ potential, we find a universal feature of the string tension and the OGE result for the Coulomb coefficient.
Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.
We study the U(2) lattice gauge theory in the pure gauge sector using the simplest action, with determinant and fundamental terms, having the naive continuum limit of SU(2)$times$U(1). We determine part of the phase diagram of the model and find a first-order critical line which goes through the U(1) critical point. We show how to deduce both the order parameter of the first-order transition and the U(2) renormalization group flow from the lattice potential in the determinant and fundamental representations. We give evidence that a Monte-Carlo simulation of the model is indeed consistent with the symmetric SU(2)$times$U(1) continuum limit in the weak coupling pertubative regime.
We discuss the gluon propagator in 3- and 4-dimensional Yang-Mills theories in Coulomb gauge and compare it with the corresponding Landau gauge propagator, showing that for both the relevant IR mass scale coincides. We also report preliminary results on Coulomb gauge ghost form factor and quark propagators and give a comment on the gluon propagators strong coupling limit.
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