arXiv subjects
Publications and source records attributed to Christof Gattringer.
We construct a novel observable for finite temperature QCD that relates confinement and chiral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate, center symmetry and the canonical ensemble.
We present recent results of our dynamical simulations with Chirally Improved fermions and report on new developments in the determination of excited light-quark meson states using interpolators constructed by applying covariant derivatives on Jacobi-smeared quark sources within the framework of the variational method.
We analytically derive a decomposition of the lattice fermion determinant for Wilson's Dirac operator with chemical potential into winding sectors, i.e., factors with a fixed number of quarks. Dividing the lattice into four domains, the determinant is factorized into terms which can be classified with respect to the winding number of the closed loops they consist of. The individual factors are expressed in terms of subdeterminants and propagators on the domains of the lattice. We numerically analyze properties of the factorization formula and discuss two applications for the determination of canonical partition functions with a fixed quark number: A speedup for the Fourier transformation technique through a dimensional reduction, and a power series expansion.
We construct efficient interpolating fields for lattice spectroscopy of mesons by applying covariant derivatives on Jacobi smeared quark sources. These interpolators are tested in a quenched calculation of excited mesons based on the variational method. We present results for pseudoscalar, scalar, vector and pseudovector mesons.
We construct a new order parameter for finite temperature QCD by considering the quark condensate for U(1)-valued temporal boundary conditions for the fermions. Fourier transformation with respect to the boundary condition defines the dual condensate. This quantity corresponds to an equivalence class of Polyakov loops, thereby being an order parameter for the center symmetry. We explore the duality relation between the quark condensate and these dressed Polyakov loops numerically, using quenched lattice QCD configurations below and above the QCD phase transition. It is demonstrated that the Dirac spectrum responds differently to changing the boundary condition, in a manner that reproduces the expected Polyakov loop pattern. We find the dressed Polyakov loops to be dominated by the lowest Dirac modes, in contrast to thin Polyakov loops investigated earlier.
In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the underlying vector theory onto two equations of the Ginsparg-Wilson (GW) type. We show that an overlap Dirac operator can be constructed which solves both GW equations simultaneously. We discuss the properties of this overlap operator and its projection onto lattice Weyl fermions which seems to be free of artefacts, in particular the projection operators are independent of the gauge field.
We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the deconfinement temperature. We analyze whether the individual Dirac eigenvector correlators differ in the confined and deconfined phases. The decay properties of the normalized Dirac eigenvector correlators turn out to be essentially identical in the two phases, but the amplitudes change. This change of the amplitudes shifts the relative contributions of the individual Dirac eigenvector correlators and is the driving mechanism for the transition from the confining static potential into the deconfining one.
We review the techniques of lattice QCD calculations for excited hadrons with light quarks and outline the future challenges that are faced in calculations with fully dynamical fermions.
We systematically compare three filtering methods used to extract topological excitations from lattice gauge configurations, namely smearing, Laplace filtering and the filtered fermionic topological charge (with chirally improved fermions). Each of these techniques introduces ambiguities, like its parameter dependence. We show, however, that all these methods can be tuned to each other over a broad range of filtering levels and that they reveal very similar topological structures. For these common structures we find an interesting power-law relating the number and packing fraction of clusters of filtered topological charge.
We study whether applying lattice projectors on a vector-like Ginsparg-Wilson Dirac operator is the only way to construct left-handed lattice fermions. Using RG transformations we derive an equation for the generating functional on the lattice, obtained by blocking from the continuum. We analyze how symmetries of the continuum theory manifest themselves in this lattice generating functional and how anomalies emerge. The formalism is applied to left-handed continuum fermions and we derive two equations that characterize the corresponding lattice symmetries. To analyze possible solutions, we directly block a parameterized action for free continuum fermions to obtain the corresponding lattice action. Subsequently we study parameter values where the continuum action corresponds to left-handed fermions.
We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all these methods, when handled with care, reveal very similar topological structures. Hence, these common structures are free of ambiguities and faithfully represent infrared degrees of freedom in the QCD vacuum. As an application we discuss an interesting power-law for the clusters of filtered topological charge.
We review our results for the simulation of the 2--d lattice Gross--Neveu model in a fermion loop representation. Possible extensions of our techniques to other models and higher dimensions are discussed, as well as the limitations of loop--type representations.
We present preliminary results of an excited state spectroscopy calculation in the 2-d lattice Gross-Neveu model. We address the construction of suitable interpolators for the variational method and their overlap with excitations. We comment on the role of the eigenvectors as a tool for matching scattering states on lattices with different volumes.
We represent thin and dressed Polyakov loops as spectral sums of eigenvalues of differential operators on the lattice. For that purpose we calculate complete sets of eigenvalues of the staggered Dirac and the covariant Laplace operator for several temporal boundary conditions. The spectra from different boundary conditions can be combined such that they represent single (thin) Polyakov loops, or a collection of loops (dressed Polyakov loops). We analyze the role of the eigenvalues in the spectral sums below and above the critical temperature.
We present results for masses of light mesons obtained with the variational method using an enhanced basis of interpolating field operators with different quark smearings. The interpolators are constructed from Jacobi-smeared quarks of a Gaussian type as well as from derivative quark sources obtained by a covariant derivative acting on the Gaussian sources. For our analysis we use quenched gauge configurations with Chirally Improved quarks and the Luescher-Weisz gauge action on a 16^3 x 32 lattice with a = 0.148 fm. We discuss the influence of derivative sources on the overlap with excited states.
Recently a formulation of overlap fermions at finite density based on an analytic continuation of the sign function was proposed. We study this proposal by analyzing the energy and number densities for free fermions as a function of the chemical potential and the temperature. Our results show that overlap fermions with chemical potential give rise to the correct continuum behavior.
We study a recently proposed formulation of overlap fermions at finite density. In particular we compute the energy density as a function of the chemical potential and the temperature. It is shown that overlap fermions with chemical potential reproduce the correct continuum behavior.
We present a numerical simulation of the Gross-Neveu model on the lattice using a new representation in terms of fermion loops. In the loop representation all signs due to Pauli statistics are eliminated completely and the partition function is a sum over closed loops with only positive weights. We demonstrate that the new formulation allows to simulate volumes which are two orders of magnitude larger than those accessible with standard methods.