arXiv subjects
Publications and source records attributed to I. Hip.
In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.
The non-normality of Wilson-type lattice Dirac operators has important consequences - the application of the usual concepts from the textbook (hermitian) quantum mechanics should be reconsidered. This includes an appropriate definition of observables and the refinement of computational tools. We show that the truncated singular value expansion is the optimal approximation to the inverse operator D^{-1} and we prove that due to the gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode expansion of the hermitian Wilson-Dirac operator.
We consider the local chirality of near-zero eigenvectors from Wilson-Dirac and clover improved Wilson-Dirac lattice operators as proposed recently by Horváth et al. We studied finer lattices and repaired for the loss of orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result we do see a clear double peak structure on lattices with resolutions higher than 0.1 fm. We found that the lattice artifacts can be considerably reduced by exploiting the biorthogonal system of left and right eigenvectors. We conclude that the dominance of instantons on topological charge fluctuations is not ruled out by local chirality measurements.
We describe an explicit construction of approximate Ginsparg-Wilson fermions for QCD. We use ingredients of perfect action origin, and further elements. The spectrum of the lattice Dirac operator reveals the quality of the approximation. We focus on beta =6 for optimisation. Such fermions are intended to be inserted into the overlap formula. Hence we also test the speed of convergence under polynomial evaluation of the overlap formula.
We re-analyze data from available finite-temperature QCD simulations near the chiral transition, with the help of Chiral Random Matrix Theory (chRMT). Statistical properties of the lowest-lying eigenvalues of the staggered Dirac operator for SU(3) lattice gauge theory with dynamical fermions are examined. We consider temperatures below, near, and above the critical temperature $T_c$ for the chiral phase transition. Below and above $T_c$ the statistics are in agreement with the exact analytical predictions in the microscopic scaling regime. Above $T_c$ we observe a gap in the spectral density and a distribution compatible with the Airy distribution. Near $T_c$ the eigenvalue correlations appear inconsistent with chRMT.
We construct a number of lattice fermions, which fulfill the Ginsparg-Wilson relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations within a short range, and study this formulation, as well as its correction to an exact Ginsparg-Wilson fermion by the ``overlap formula''. Then we suggest a new method to realize this correction perturbatively, without using the tedious square root operator. In this way we combine many favorable properties: good chiral behavior, small mass renormalization, excellent scaling and rotational invariance, as well as a relatively modest computational effort, which makes such formulations most attractive for QCD.
We compare the lower edge spectral fluctuations of the staggered lattice Dirac operator for the Schwinger model with the predictions of chiral Random Matrix Theory (chRMT). We verify their range of applicability, checking in particular the role of non-trivial topological sectors and the flavor symmetry of the staggered fermions for finite lattice spacing. Approaching the continuum limit we indeed find clear signals for topological modes in the eigenvalue spectrum. These findings indicate problems in the verification of the chRMT predictions.
We test exact and approximate Ginsparg-Wilson fermions with respect to their chiral and scaling behavior in the 2-flavor Schwinger model. We first consider explicit approximate GW fermions in a short range, then we proceed to their chiral correction by means of the ``overlap formula'', and finally we discuss a numerically efficient perturbative chiral correction. In this way we combine very good chiral and scaling properties with a relatively modest computational effort.
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT).
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate.
Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed point Dirac operator investigating also microscopic fluctuations and fermion condensation.
We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.
We discuss the interplay between topologically non-trivial gauge field configurations and the spectrum of the Wilson-Dirac operator in lattice gauge theory. Our analysis is based on analytic arguments and numerical results from a lattice simulation of QED_2.
We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion species of identical mass. In the simulation we are using Wilson fermions where chiral symmetry is explicitly broken. Since there is no known simple order parameter it is non-trivial to identify the critical line of the chiral phase transition. We therefore need to find observables which allow an identification of a possible restoration of chiral symmetry. We utilize the PCAC-relations in order to identify the critical coupling, where chiral symmetry is restored.
We investigate the interplay between topological charge and the spectrum of the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo simulations with dynamical fermions. A new theorem on the spectral decomposition of the fermion matrix establishes that its real eigenvalues (and corresponding eigenvectors) play a role similar to the zero eigenvalues (zero modes) of the Dirac operator in continuous background fields. Using numerical techniques we concentrate on studying the real part of the spectrum. These results provide new insights into the behaviour of physical quantities as a function of the topological charge. In particular we discuss fermion determinant, effective action and pseudoscalar densities.
Using the geometric definition of the topological charge we decompose the path integral of 2-dimensional U(1) lattice gauge theory into topological sectors. In a Monte Carlo simulation we compute the average value of the action as well as the distribution of its values for each sector separately. These numbers are compared with analytic lower bounds of the action which are relevant for classical configurations carrying topological charge. We find that quantum fluctuations entirely dominate the path integral. Our results for the probability distribution of the Monte Carlo generated configurations among the topological sectors can be understood by a semi-phenomenological argument.
Lüscher has suggested a method to determine phase shifts from the finite volume dependence of the two-particle energy spectrum. We apply this to two models in d=2: (a) the Ising model, (b) a system of two Ising fields with different mass and coupled through a 3-point term, both considered in the symmetric phase. The Monte Carlo simulation makes use of the cluster updating and reduced variance operator techniques. For the Ising system we study in particular O($a^2$) effects in the phase shift of the 2-particle scattering process.