arXiv subjects
Publications and source records attributed to Anna Hasenfratz.
Smeared link fermionic actions can be straightforwardly simulated with partial-global updating. The efficiency of this simulation is greatly increased if the fermionic matrix is written as a product of several near-identical terms. Such a break-up can be achieved using polynomial approximations for the fermionic matrix. In this paper we will focus on methods of determining the optimum polynomials.
We performed dynamical simulations with HYP smeared staggered fermions using the recently proposed partial-global stochastic Metropolis algorithm with fermion matrix reduction and determinant breakup improvements. In this paper we discuss our choice of the action parameters and study the autocorrelation time both with four and two fermionic flavors at different quark mass values on approximately 10 fm^4 lattices. We find that the update is especially efficient with two flavors making simulations on larger volumes feasible.
We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of ratios of fermionic determinants is essential for a recently proposed updating method of smeared link dynamical fermions. This update creates a sequence of configurations by changing a subset of the gauge links by a pure gauge heat bath or over relaxation step. The acceptance of the proposed configuration depends on the ratio of the fermionic determinants on the new and original configurations. We study this ratio as the function of the number of links that are changed in the heat bath update. We find that even when every link of a given direction and parity of a 10fm^4 configuration is updated, the average of the determinant ratio is still close to one and with the improved stochastic estimator the proposed change is accepted with about 20% probability. This improvement suggests that the new updating technique can be efficient even on large lattices.
Staggered fermions with smeared links can have greatly improved chiral properties. In a recent paper we introduced a simple and effective method to simulate four flavors of staggered smeared link fermions. In this work we extend the four flavor method to two flavors. We define the two flavor action by the square root of the four flavor fermionic determinant and show that by using a polynomial approximation the two flavor action can be evaluated with the necessary accuracy. We test this method by studying the finite temperature phase structure with hypercubic smeared (HYP) link staggered action on N_t=4 temporal lattices.
The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends quadratically on the pion mass, approaching zero in the chiral limit. Lattice calculations have difficulty reproducing this behavior. In this paper we study the topological susceptibility on dynamical staggered fermion configurations. Our results indicate that the lattice spacing has to be small, around a~0.1fm for thin link staggered fermion actions to show the expected chiral behavior. Our preliminary result indicates that fat link fermions, on the other hand, reproduce the theoretical expectations even on lattices with a~0.17fm. We argue that this is due to the improved flavor symmetry of fat link fermionic actions.
We comment on the recent paper (hep-lat/0102003) by Horvath, Isgur, McCune, and Thacker, which concludes that the local chiral structure of fermionic eigenmodes is not consistent with instanton dominance. Our calculations, done with an overlap action, suggest the opposite conclusion.
We explore the properties of low lying eigenmodes of fermions in the quenched approximation of lattice QCD. The fermion action is a recently proposed overlap action and has exact chiral symmetry. We find that chiral zero-eigenvalue modes are localized in space and their positions correlate strongly with the locations (as defined through the density of pure gauge observables) of instantons of the appropriate charge. Nonchiral modes are also localized with peaks which are strongly correlated with the positions of both charges of instantons. These correlations slowly die away as the fermion eigenvalue rises. Correlators made of quark propagators restricted to these modes closely reproduce ordinary hadron correlators at small quark mass in many channels. Our results are in qualitative agreement with the expectations of instanton liquid models.
We test a recently proposed improved lattice-fermion action, the fat link clover action, examining indicators of pathological small-quark-mass lattice artifacts ("exceptional configurations") on quenched lattices of spacing 0.12 fm and studying scaling properties of the light hadron spectrum for lattice spacing a=0.09 and 0.16 fm. We show that the action apparently has fewer problems with pathological lattice artifacts than the conventional nonperturbatively improved clover action and its spectrum scales just as well.
We study the spatial correlator of the topological charge density operator in pure SU(3) gauge theory and in two flavor QCD. We show that the data for distances up to about 1 fm is consistent with a vacuum consisting of individual instantons and closely bound pairs. The percentage of paired objects is twice as large on the dynamical configurations than on the pure gauge ones, implying increased molecule formations due to fermionic interactions.
We study exceptional modes of both the Wilson and the clover action in order to understand why quenched clover spectroscopy suffers so severely from exceptional configurations. We show that a large clover coefficient can make the exceptional modes extremely localized and thus very sensitive to short distance fluctuations. We contrast this with the case of the Wilson action where exceptional modes correspond to large instantons. These modes are broadly extended and suffer much less from discretization errors.
We describe a way to optimize the chiral behavior of Wilson-type lattice fermion actions by studying the low energy real eigenmodes of the Dirac operator. We find a candidate action, the clover action with fat links with a tuned clover term. The action shows good scaling behavior at Wilson gauge coupling beta=5.7.
We describe a way to optimize the chiral behavior of Wilson-type lattice fermion actions by studying the low energy real eigenmodes of the Dirac operator. We find a candidate action, the clover action with fat links with a tuned clover term. We present a calculation of spectroscopy and matrix elements at Wilson gauge coupling $β=5.7$. The action shows good scaling behavior.
We study the topological content of the SU(3) vacuum using the renormalization group (RG) mapping method. RG mapping is a simple smoothing algorithm, in which a series of APE-smearing steps are done while the topological content of the configuration is carefully monitored. This monitoring process makes it possible to separate true topological objects from vacuum fluctuations and allows an extrapolation to zero smearing steps. Using RG mapping we have measured the instanton distribution and topological susceptibility for SU(3) gauge theory. We arrive at a value for the topological susceptibily, $χ^{1/4}$ of 203(5) MeV. The size distribution peaks at $ρ=0.3$fm, and is in good agreement with the prediction of instanton liquid models.
This talk is a review of our studies of instantons and their properties as seen in our lattice simulations of SU(2) gauge theory. We have measured the topological susceptibility and the size distribution of instantons in the QCD vacuum. We have also investigated the properties of quarks moving in instanton background field configurations, where the sizes and locations of the instantons are taken from simulations of the full gauge theory. By themselves, these multi-instanton configurations do not confine quarks, but they induce chiral symmetry breaking.
In this paper we derive a simple parametrization of the cycling method developed by us in our earlier work. The new method, called renormalization group (RG) mapping, consists of a series of carefully tuned APE-smearing steps. We study the relation between cycling and RG mapping. We also investigate in detail how smooth instantons and instanton-anti-instanton pairs behave under the RG mapping transformation. We use the RG mapping technique to study the topological susceptibility and instanton size distribution of SU(2) gauge theory. We find scaling in both quantities in a wide range of coupling values. Our result for the topological susceptibility, chi^1/4=220(6) MeV, agrees with our earlier results.
We describe quenched spectroscopy in SU(2) gauge theory using smoothed gauge field configurations. We investigate the properties of quarks moving in instanton background field configurations, where the sizes and locations of the instantons are taken from simulations of the full gauge theory. By themselves, these multi-instanton configurations do not confine quarks, but they induce chiral symmetry breaking.
We study the topological content of the vacuum of SU(2) pure gauge theory using lattice simulations. We use a smoothing process based on the renormalization group equation. This removes short distance fluctuations but preserves long distance structure. The action of the smoothed configurations is dominated by instantons, but they still show an area law for Wilson loops with an unchanged string tension. The average radius of an instanton is about 0.2 fm, at a density of about 2 fm${}^{-4}$.
We study the topological content of the vacuum of SU(2) pure gauge theory using lattice simulations. We use a smoothing process based on the renormalization group equation which removes short distance fluctuations but preserves long distance structure. The action of the smoothed configurations is dominated by instantons, but they still show an area law for Wilson loops with a string tension equal to the string tension on the original configurations. Yet it appears that instantons are not directly responsible for confinement. The average radius of an instanton is about 0.2 fm, at a density of about 2 fm^(-4). This is a much smaller average size than other lattice studies have indicated. The instantons appear not to be randomly distributed in space, but are clustered.