arXiv subjects

Roland Hoffmann

Publications and source records attributed to Roland Hoffmann.

At least 19 recordsLinked to original sources

arXiv2008

Epsilon regime calculations with reweighted clover fermions

We perform fully dynamical simulations at small quark masses by reweighting in the quark mass, calculating the weight factors stochastically. This approach avoids some of the technical difficulties associated with direct simulations. We find that the weight factors fluctuate only moderately on nHYP smeared dynamical Wilson-clover ensembles, and demonstrate that the overlap between the original and reweighted configurations is large both for short and long distance observables. We could successfully reweight 16^4, (1.85fm)^4 volume configurations from m_q 20 MeV to m_q~5 MeV, and 24^4, (2.77fm)^4 configurations from m_q~8MeV to m_q~MeV quark masses, reaching the epsilon-regime. Using the pseudoscalar and axialvector correlators we predict the low energy constants Sigma and F and study their volume and mass dependence.

hep-lat↗

arXiv2008

Low energy chiral constants from epsilon-regime simulations with improved Wilson fermions

We present a lattice QCD calculation of the low energy constants of the leading order chiral Lagrangian. In these simulations the epsilon regime is reached by using tree-level improved nHYP Wilson fermions combined with reweighting in the quark mass. We analyze two point functions on two ensembles with lattices of size (1.85fm)^4 and (2.8fm)^4, and at several quark mass values between 4 and 20 MeV. The data are well fitted with next-to-leading order chiral perturbative formulae and predict F=90(4)MeV and Sigma^(1/3)=248(6)MeV in the MS-bar scheme at 2 GeV.

hep-lat↗

arXiv2008

Reweighting towards the chiral limit

We propose to perform fully dynamical simulations at small quark masses by reweighting in the quark mass. This approach avoids some of the technical difficulties associated with direct simulations at very small quark masses. We calculate the weight factors stochastically, using determinant breakup and low mode projection to reduce the statistical fluctuations. We find that the weight factors fluctuate only moderately on nHYP smeared dynamical Wilson-clover ensembles, and we could successfully reweight 16^4, (1.85fm)^4 volume configurations from m_q = 20MeV to m_q = 5MeV quark masses, reaching the epsilon-regime. We illustrate the strength of the method by calculating the low energy constant F from the epsilon-regime pseudo-scalar correlator.

hep-lat↗

arXiv2007

More about QCD on compact spaces

We present some results about spontaneous breaking of global symmetries for four-flavor, three color QCD on compact spaces with two short directions. When the two short directions have equal length and identical boundary conditions, there is a single transition. When the two short directions have boundary conditions of opposite parity and are of roughly equal extent, the C-breaking and deconfinement transitions separate. When the two short dimensions are of different length, the transitions are modified in qualitative agreement with expectations from dimensional reduction. These features resemble the situation in pure gauge simulations at small and large number of colors.

hep-lat↗

arXiv2007

Non-perturbative improvement of nHYP smeared Wilson fermions

Using Schroedinger functional techniques, we determine the coefficient of the clover term necessary for non-perturbative O(a) improvement of hypercubic smeared Wilson fermions on a quenched plaquette action background. Unlike for unsmeared Wilson fermions, the resulting clover coefficients are close to the tree-level value even at coarse lattice spacings, indicating the absence of large cutoff effects. A number of exploratory tests are also performed with the improved action.

hep-lat↗

arXiv2007

The impact of localized overlap eigenmodes on RMT measurements and topology

The low energy eigenmodes of the continuum QCD Dirac operator are extended, but on the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes. These non-physical modes can introduce strong lattice artifacts for observables that are sensitive to chiral symmetry, especially in mixed action simulations. We study how these lattice artifacts depend on the parameters of the overlap operator and their affect on the distribution on the Dirac eigenmodes and the topological susceptibility.

hep-lat↗

arXiv2007

Dynamical simulations with HYP-link Wilson fermions

We present results from simulations of two dynamical flavors of improved Wilson fermions with nHYP smeared gauge links. We demonstrate that the simulation is stable at a pseudo-scalar mass of 360MeV, a 2.1fm box and a lattice spacing of 0.13fm.

hep-lat↗

arXiv2007

Localized eigenmodes of the overlap operator and their impact on the eigenvalue distribution

In a system where chiral symmetry is spontaneously broken, the low energy eigenmodes of the continuum Dirac operator are extended. On the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes that affect physical quantities sensitive to chiral symmetry. While the infrared eigenmodes of the Wilson Dirac operator are usually extended even on coarse lattices, the chiral overlap operator has many localized eigenmodes in the physical region, especially in mixed action simulations. Depending on their density, these modes can introduce strong lattice artifacts. The effect can be controlled by changing the parameters of the overlap operator, in particular the clover improvement term and the center of the overlap projection.

hep-lat↗

arXiv2007

Hypercubic Smeared Links for Dynamical Fermions

We investigate a variant of hypercubic gauge link smearing where the SU(3) projection is replaced with a normalization to the corresponding unitary group. This smearing is differentiable and thus suitable for use in dynamical fermion simulations using molecular dynamics type algorithms. We show that this smearing is as efficient as projected hypercubic smearing in removing ultraviolet noise from the gauge fields. We test the normalized hypercubic smearing in dynamical improved (clover) Wilson and valence overlap simulations.

hep-lat↗

arXiv2007

Quark condensate in one-flavor QCD

We compute the condensate in QCD with a single quark flavor using numerical simulations with the overlap formulation of lattice fermions. The condensate is extracted by fitting the distribution of low lying eigenvalues of the Dirac operator in sectors of fixed topological charge to the predictions of Random Matrix Theory. Our results are in excellent agreement with estimates from the orientifold large-N_c expansion.

hep-th↗

arXiv2006

QCD with one compact spatial dimension

The realization of global symmetries can depend on the geometry of the underlying space. In particular, compactification can lead to spontaneous breaking of such symmetries. Four-dimensional QCD with fundamental representation fermions embedded in a space with one compact spatial dimension has a critical length, at which the theory undergoes a phase transition and develops a ground state that is no longer charge conjugation invariant. We show this behavior with simulations of three color, four flavor QCD. We use unrooted staggered fermion at two values of the lattice spacing and several quark masses. We discuss the dependence of the transition on the dynamical fermion mass as well as its connection to the finite temperature and chiral phase transitions.

hep-lat↗

arXiv2006

The chiral condensate on 2-flavor staggered configurations from an overlap operator

We measure the low lying eigenmodes of an overlap Dirac operator on 2--flavor staggered configurations. By comparing the eigenmode distribution to the predictions of Random Matrix Theory we test to what accuracy staggered configurations describe continuum QCD. The agreement between the numerical data and RMT implies that at our quark mass values the lattice artifacts of the staggered configurations are comparable to overlap configurations. We identify the overlap valence mass that best matches the staggered sea quarks and predict the value of the infinite volume 2-flavor chiral condensate.

hep-lat↗

arXiv2006

Mixed Action Simulations on Staggered Background; Interpretation and Result for the 2-flavor QCD Chiral Condensate

Growing evidence indicates that in the continuum limit the rooted staggered action is in the correct QCD universality class, the non-local terms arising from taste breaking can be viewed as lattice artifacts. In this paper we consider the 2-flavor Asqtad staggered action at a lattice spacing of approximately 0.13 fm and probe the properties of the staggered configurations by an overlap valence Dirac operator. By comparing the distribution of the overlap eigenmodes to continuum QCD predictions we investigate if/when the lattice artifacts are small as a function of the staggered quark mass. We define a matching overlap quark mass where the lattice corrections are minimal for the topological susceptibility and from the eigenmode distribution we predict the 2-flavor chiral condensate. Our results indicate that the staggered configurations are consistent with 2-flavor continuum QCD up to small lattice artifacts, and predict a consistent value for the infinite volume chiral condensate.

hep-lat↗

arXiv2006

The rooted staggered determinant in the Schwinger model

We investigate the continuum limit of the rooted staggered action in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinants with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the difference of the staggered and overlap fermion actions. We show that this residue scales at least as O(a^2), implying that any difference, be it local or non-local, between the staggered and overlap actions becomes irrelevant in the continuum limit. For the model under consideration here, this observation justifies the rooting procedure for the staggered sea quark action.

hep-lat↗

arXiv2006

Validity of the Rooted Staggered Determinant in the continuum limit

We investigate the continuum limit of the rooted staggered determinant in the 2-dimensional Schwinger model. We match both the unrooted and rooted staggered determinant with an overlap fermion determinant of two (one) flavors and a local pure gauge effective action by fitting the coefficients of the effective action and the mass of the overlap operator. The residue of this fit measures the difference of the staggered and overlap fermion actions. We show that this residue scales at least as O(a^2), implying that any difference, be it local or non-local, between the staggered and overlap actions becomes irrelevant in the continuum limit. This observation justifies the rooting procedure.

hep-lat↗

arXiv2005

Chiral properties of dynamical Wilson fermions

We consider two-flavor QCD in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken at order a and hence the isovector axial currents require improvement as well as a finite renormalization if they are to satisfy continuum Ward--Takahashi identities up to small lattice corrections of O(a^2). Algorithmic difficulties at coarse lattice spacings, where HMC suffers from a distorted Dirac spectrum, are discussed. This is shown to be a cutoff effect, which disappears rapidly as the lattice spacing is decreased. An alternative algorithm, the polynomial hybrid Monte Carlo algorithm, is found to perform significantly better in the presence of exceptionally small eigenvalues. Extending previously used methods both the improvement and the renormalization of the axial current are implemented non--perturbatively in terms of correlation functions formulated in the framework of the Schroedinger functional. In both cases this is achieved by enforcing continuum Ward identities at finite lattice spacing. Together, this restores the isovector chiral symmetry to quadratic order in the lattice spacing. With little additional effort the normalization factor of the local vector current is also obtained.

hep-lat↗

arXiv2005

Restoring chiral symmetry to O(a^2) for dynamical Wilson fermions

We present results for the non-perturbative determination of the improvement and renormalization factors of the isovector axial current for lattice QCD with two flavors of dynamical Wilson quarks. The improvement and normalization conditions are formulated in terms of matrix elements of the PCAC relation in the Schroedinger functional setup and results are given in the form of interpolating formulae for bare gauge couplings beta=6/g_0^2>5.2.

hep-lat↗

arXiv2005

Towards a non-perturbative computation of the RGI strange quark mass with two dynamical flavors

The non-perturbative running of the quark mass in the Schroedinger functional scheme is computed over a large energy range (covering scales differing by two orders of magnitude). This allows to relate lattice estimates of the running quark mass to the renormalization group invariant mass. The result is used in a preliminary computation of the strange quark mass in the theory with two flavors of non-perturbatively improved Wilson quarks. A more detailed discussion of the calculation can be found in [1].

hep-lat↗