Considerations on Neuberger's operator
We discuss new approaches to the numerical implementation of Neuberger's operator for lattice fermions and the possible use of block spin transformations.
hep-lat↗
arXiv subjects
C. Rebbi
Publications and source records attributed to C. Rebbi.
Potential between external monopole and antimonopole in SU(2) lattice glu odynamics
We present the results of a study of the free energy of a monopole pair in pure SU(2) theory at finite temperature, both below and above the deconfinement tran sition. We find a Yukawa potential between monopoles in both phases. At low temp erature, the screening mass is compatible with the lightest glueball mass. At hi gh temperature, we observe an increased screening mass with no apparent disconti nuity at the phase transition.
hep-lat↗
Periodic Instantons in SU(2) Yang-Mills-Higgs Theory
The properties of periodic instanton solutions of the classical SU(2) gauge theory with a Higgs doublet field are described analytically at low energies, and found numerically for all energies up to and beyond the sphaleron energy. Interesting new classes of bifurcating complex periodic instanton solutions to the Yang-Mills-Higgs equations are described.
hep-ph↗
Tunneling of Bound Systems at Finite Energies: Complex Paths Through Potential Barriers
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical systems. Even for systems initially in their ground state, not generally describable in semiclassical terms, the transmission probability has a semiclassical (exponential) form. The calculation of the tunneling exponent uses analytic continuation of degrees of freedom into a complex phase space as well as analytic continuation of the classical equations of motion into the complex time plane. We test this semiclassical technique by comparing its results with those of a computational investigation of the full quantum mechanical system, finding excellent agreement.
quant-ph↗
The Semiclassical Description of Tunneling in Scattering with Multiple Degrees of Freedom
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a semiclassical technique developed in the context of instanton-like transitions in quantum field theory. This latter technique is based on an analytic continuation of the degrees of freedom into a complex phase space, and the simultaneous analytic continuation of the equations of motion into the complex time plane.
hep-ph↗
Free energy of an SU(2) monopole-antimonopole pair
We induce an external ${Z}_2$ monopole-antimonopole pair in an SU(2) lattice gauge system and measure its free energy as a way to probe the vacuum structure. We discuss the motivation and computational methodology of the investigation and illustrate our preliminary results.
hep-lat↗
QCDF90: Lattice QCD with Fortran 90
We have used Fortran 90 to implement lattice QCD. We have designed a set of machine independent modules that define fields (gauge, fermions, scalars, etc...) and overloaded operators for all possible operations between fields, matrices and numbers. With these modules it is very simple to write high-level efficient programs for QCD simulations. To increase performances our modules also implements assignments that do not require temporaries, and a machine independent precision definition. We have also created a useful compression procedure for storing the lattice configurations, and a parallel implementation of the random generators. We have widely tested our program and modules on several parallel and single processor supercomputers obtaining excellent performances.
hep-lat↗
Critical properties and monopoles in U(1) lattice gauge theory
We present a detailed study of the properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term, for values of the monopole coupling $λ$ such that the transition is of second order. By a finite size analysis we show that at $λ= 0.9$ the critical exponent is already characteristic of a second-order transition. Moreover, we find that this exponent is definitely different from the one of the Gaussian case. We further observe that the monopole density becomes approximately constant in the second-order region. Finally we reveal the unexpected phenomenon that the phase transition persists up to very large values of $λ$, where the transition moves to (large) negative $β$.
hep-lat↗
QCDF90: A set of Fortran 90 modules for a high-level, efficient implementation of QCD simulations
We present a complete set of Fortran 90 modules that can be used to write very compact, efficient, and high level QCD programs. The modules define fields (gauge, fermi, generators, complex, and real fields) as abstract data types, together with simpler objects such as SU(3) matrices or color vectors. Overloaded operators are then defined to perform all possible operations between the fields that may be required in a QCD simulation. QCD programs written using these modules need not have cumbersome subroutines and can be very simple and transparent. This is illustrated with two simple example programs.
hep-lat↗
The Taming of QCD by Fortran 90
We implement lattice QCD using the Fortran 90 language. We have designed machine independent modules that define fields (gauge, fermions, scalars, etc...) and have defined overloaded operators for all possible operations between fields, matrices and numbers. With these modules it is very simple to write QCD programs. We have also created a useful compression standard for storing the lattice configurations, a parallel implementation of the random generators, an assignment that does not require temporaries, and a machine independent precision definition. We have tested our program on parallel and single processor supercomputers obtaining excellent performances.
hep-lat↗
Towards a lattice calculation of the coefficients of the QCD chiral Lagrangian
We discuss a general strategy to compute the coefficients of QCD chiral Lagrangian by using the lattice regularization of QCD with Wilson fermions. This procedure requires the introduction of an effective Lagrangian for lattice QCD as an intermediate step in the calculation. The continuum QCD chiral Lagrangian can be then obtained by expanding the lattice effective Lagrangian in increasing powers of the external momenta. A suitable renormalization procedure is required to account for the chiral symmetry breaking introduced by the Wilson term in the lattice action. In anticipation of a numerical simulation, the lattice effective Lagrangian is computed analytically and investigated in the strong coupling and large $N$ limit
hep-lat↗
QCD chiral Lagrangian on the lattice, strong coupling expansion and Ward identities with Wilson fermions
We discuss a general strategy to compute the coefficients of the QCD chiral Lagrangian using lattice QCD with Wilson fermions. This procedure requires the introduction of a lattice chiral Lagrangian as an intermediate step in the calculation. The QCD chiral Lagrangian is then obtained by expanding the lattice effective theory in increasing powers of the lattice spacing and the external momenta. In order to investigate the consequences of the chiral symmetry breaking induced by the Wilson term, we study the lattice chiral Lagrangian at the leading order of the strong coupling and large $N$ expansion. We show that the effects of the Wilson term can be conveniently taken into account, in the lattice effective theory, by a suitable renormalization procedure. In particular, we show that, at the leading order of the strong coupling and large N expansion, the chiral symmetry is exactly recovered on the lattice provided that the bare quark mass and the lattice operators are properly renormalized.
hep-lat↗
Critical behavior and monopole density in U(1) lattice gauge theory
Our study of the energy distribution has shown that the strength of the first order transition in the four-dimensional compact U(1) lattice gauge theory decreases when the coupling $λ$ of the monopole term increases. The disappearance of the energy gap for sufficiently large values of $λ$ indicates that the transition ultimately becomes of second order. In our present investigation, based on a finite-size analysis, we show that already at $λ= 0.9$ the critical exponent is characteristic of a second-order transition. Interestingly, this exponent turns out to be definitely different from that of the Gaussian case. We observe that the monopole density becomes constant in the second order region. In addition we find the rather surprising result that the phase transition persists up to very large values of $λ$, where the transition moves to (large) negative $β$.
hep-lat↗
Order parameters and boundary effects in U(1) lattice gauge theory
We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an ``infinite'' current network, with an appropriate definition of ``infinite'' for the various types of boundary conditions imposed on the finite lattice. The probability for the occurrence of an ``infinite'' network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.
hep-lat↗
Characterization of phases and boundary effects in U(1) gauge theory
We show that the two phases of the 4-dimensional compact U(1) lattice gauge theory are characterized by the existence or absence of an infinite current network, defining ``infinite'' on a finite lattice in a manner appropriate to the chosen boundary conditions. In addition for open and fixed boundary conditions we demonstrate the effects of inhomogeneities and provide examples of the reappearance of an energy gap.
hep-lat↗
Phase transition and dynamical-parameter method in U(1) gauge theory
Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge theory in the neighborhood of the transition point are made difficult by the suppression of tunneling between the phases, which becomes very strong as soon as the volume of the lattice grows to any appreciable size. This problem can be avoided by making the monopole coupling a dynamical variable. In this manner one can circumvent the tunneling barrier by effectively riding on top of the peaks in the energy distribution which meet for sufficiently large monopole coupling. Here we present an efficient method for determining the parameters needed for this procedure, which can thus be implemented at low computational cost also on large lattices. This is particularly important for a reliable determination of the transition point. We demonstrate the working of our method on a 16^4 lattice. We obtain an equidistribution of configurations across the phase transition even for such a relatively large lattice size.
hep-lat↗
Monopole currents and Dirac sheets in U(1) lattice gauge theory
We show that the phases of the 4-dimensional compact U(1) lattice gauge theory are unambiguously characterized by the topological properties of minimal Dirac sheets as well as of monopole currents lines. We obtain the minimal sheets by a simulated-annealing procedure. Our results indicate that the equivalence classes of sheet structures are the physical relevant quantities and that intersections are not important. In conclusion we get a percolation-type view of the phases which holds beyond the particular boundary conditions used.
hep-lat↗
Topological structures and phases in U(1) gauge theory
We show that topological properties of minimal Dirac sheets as well as of currents lines characterize the phases unambiguously. We obtain the minimal sheets reliably by a suitable simulated-annealing procedure.
hep-lat↗