arXiv subjects

N. Cundy

Publications and source records attributed to N. Cundy.

At least 19 recordsLinked to original sources

arXiv2015

Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions

We study the deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions. Our simulations have been carried out on a $16^3 \times 6$ lattice at a pion mass around 500 MeV with a special HMC algorithm without any approximation such as fixed topology. We consider several temperatures from 220 MeV which is close to the deconfinement to 280 MeV which is above it. The dependence of the Polyakov loop, the chiral condensate, the Dirac spectra and the connected part of chiral susceptibility on the inverse gauge coupling has been studied. Our data indicates that the transition point lies between $β= 7.6$ and $β= 8.1$, but a more precise determination is not possible with our present statistics.

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arXiv2014

Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field

We study the influence of an external magnetic field on the deconfinement transition in two-flavour lattice QCD with physical quark charges. We use dynamical overlap fermions without any approximation such as fixed topology and perform simulations on a $16^3 \times 6$ lattice and at a pion mass around $500MeV$. The pion mass (as well as the lattice spacing) was determined in independent runs on $12^3 \times 24$ lattices. We consider two temperatures, one of which is close to the deconfinement transition and one which is above. Within our limited statistics the dependence of the Polyakov loop and chiral condensate on the magnetic field supports the "inverse magnetic catalysis" scenario in which the transition temperature decreases as the field strength grows for temperature not to far above the critical temperature.

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arXiv2011

QCD in the delta-Regime

The delta-regime of QCD is characterised by light quarks in a small spatial box, but a large extent in (Euclidean) time. In this setting a specific variant of chiral perturbation theory - the delta-expansion - applies, based on a quantum mechanical treatment of the quasi one-dimensional system. In particular, for vanishing quark masses one obtains a residual pion mass M_pi^R, which has been computed to the third order in the delta-expansion. A comparison with numerical measurements of this residual mass allows for a new determination of some Low Energy Constants, which appear in the chiral Lagrangian. We first review the attempts to simulate 2-flavour QCD directly in the delta-regime. This is very tedious, but results compatible with the predictions for M_pi^R have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the delta-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constant \bar l_3.

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arXiv2010

Exploring the Nucleon Structure from First Principles of QCD

Quantum Chromodynamics (QCD) is generally assumed to be the fundamental theory underlying nuclear physics. In recent years there is progress towards investigating the nucleon structure from first principles of QCD. Although this structure is best revealed in Deep Inelastic Scattering, a consistent analysis has to be performed in a fully non-perturbative scheme. The only known method for this purpose are lattice simulations. We first sketch the ideas of Monte Carlo simulations in lattice gauge theory. Then we comment in particular on the issues of chiral symmetry and operator mixing. Finally we present our results for the Bjorken variable of a single quark, and for the second Nachtmann moment of the nucleon structure functions.

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arXiv2010

Tuning the strange quark mass in lattice simulations

QCD lattice simulations with 2+1 flavours typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass to its physical value and then the up-down quark mass. An alternative method of tuning the quark masses is discussed here in which the singlet quark mass is kept fixed, which ensures that the kaon always has mass less than the physical kaon mass. It can also take into account the different renormalisations (for singlet and non-singlet quark masses) occurring for non-chirally invariant lattice fermions and so allows a smooth extrapolation to the physical quark masses. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Results show the correct order for the baryon octet and decuplet spectrum and an extrapolation to the physical pion mass gives mass values to within a few percent of their experimental values.

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arXiv2009

Quark structure from the lattice Operator Product Expansion

We have reported elsewhere in this conference on our continuing project to determine non-perturbative Wilson coefficients on the lattice, as a step towards a completely non-perturbative determination of the nucleon structure. In this talk we discuss how these Wilson coefficients can be used to extract Nachtmann moments of structure functions, using the case of off-shell Landau-gauge quarks as a first simple example. This work is done using overlap fermions, because their improved chiral properties reduce the difficulties due to operator mixing.

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arXiv2009

Results from 2+1 flavours of SLiNC fermions

QCD results are presented for a 2+1 flavour fermion clover action (which we call the SLiNC action). A method of tuning the quark masses to their physical values is discussed. In this method the singlet quark mass is kept fixed, which solves the problem of different renormalisations (for singlet and non-singlet quark masses) occuring for non-chirally invariant lattice fermions. This procedure enables a wide range of quark masses to be probed, including the case with a heavy up-down quark mass and light strange quark mass. Preliminary results show the correct splittings for the baryon (octet and) decuplet spectrum.

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arXiv2009

A Non-Perturbative Operator Product Expansion

Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photon momenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This over-determines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.

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arXiv2009

Non-perturbative improvement of stout-smeared three flavour clover fermions

We discuss a 3-flavour lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory.

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arXiv2008

Numerical Methods for the QCD Overlap Operator IV: Hybrid Monte Carlo

The extreme computational costs of calculating the sign of the Wilson matrix within the overlap operator have so far prevented four dimensional dynamical overlap simulations on realistic lattice sizes, because the computational power required to invert the overlap operator, the time consuming part of the Hybrid Monte Carlo algorithm, is too high. In this series of papers we introduced the optimal approximation of the sign function and have been developing preconditioning and relaxation techniques which reduce the time needed for the inversion of the overlap operator by over a factor of four, bringing the simulation of dynamical overlap fermions on medium-size lattices within the range of Teraflop-computers. In this paper we adapt the HMC algorithm to overlap fermions. We approximate the matrix sign function using the Zolotarev rational approximation, treating the smallest eigenvalues of the Wilson operator exactly within the fermionic force. We then derive the fermionic force for the overlap operator, elaborating on the problem of Dirac delta-function terms from zero crossings of eigenvalues of the Wilson operator. The crossing scheme proposed shows energy violations which are better than O($Δτ^2$) and thus are comparable with the violations of the standard leapfrog algorithm over the course of a trajectory. We explicitly prove that our algorithm satisfies reversibility and area conservation. Finally, we test our algorithm on small $4^4$, $6^4$, and $8^4$ lattices at large masses.

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arXiv2008

Clover improvement for stout-smeared 2+1 flavour SLiNC fermions: non-perturbative results

We discuss an action in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover coefficient, csw, has to be tuned. We present here preliminary results of a non-perturbative determination of csw using the Schrodinger functional and as a by-product also a determination of the critical hopping parameter. A determination of the renormalisation constant for the local vector current is also given. Comparisons of the results are made with lowest order perturbation theory results.

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arXiv2008

Nucleon structure in terms of OPE with non-perturbative Wilson coefficients

Lattice calculations could boost our understanding of Deep Inelastic Scattering by evaluating moments of the Nucleon Structure Functions. To this end we study the product of electromagnetic currents between quark states. The Operator Product Expansion (OPE) decomposes it into matrix elements of local operators (depending on the quark momenta) and Wilson coefficients (as functions of the larger photon momenta). For consistency with the matrix elements, we evaluate a set of Wilson coefficients non-perturbatively, based on propagators for numerous momentum sources, on a 24^3 x 48 lattice. The use of overlap quarks suppresses unwanted operator mixing and lattice artifacts. Results for the leading Wilson coefficients are extracted by means of Singular Value Decomposition.

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arXiv2007

The operator product expansion on the lattice

We investigate the Operator Product Expansion (OPE) on the lattice by directly measuring the product (where J is the vector current) and comparing it with the expectation values of bilinear operators. This will determine the Wilson coefficients in the OPE from lattice data, and so give an alternative to the conventional methods of renormalising lattice structure function calculations. It could also give us access to higher twist quantities such as the longitudinal structure function F_L = F_2 - 2 x F_1. We use overlap fermions because of their improved chiral properties, which reduces the number of possible operator mixing coefficients.

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arXiv2007

Dynamical overlap fermions with increased topological tunnelling

We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new method of differentiating the eigenvectors of the Kernel operator, which removes an instability in the fermionic force. Secondly, by simulating part of the fermion determinant exactly, without pseudo-fermions, we are able to increase the rate of topological tunnelling by a factor of more than ten, reducing the auto-correlation.

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arXiv2005

Improving the dynamical overlap algorithm

We present algorithmic improvements to the overlap Hybrid Monte Carlo algorithm, including preconditioning techniques and improvements to the correction step, used when one of the eigenvalues of the Kernel operator changes sign, which is now O(Δt^2) exact.

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arXiv2004

Dynamical overlap simulations using HMC

We apply the Hybrid Monte Carlo method to the simulation of overlap fermions. We give the fermionic force for the molecular dynamics update. We present early results on a small dynamical chiral ensemble.

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arXiv2004

Improving Inversions of the Overlap Operator

We present relaxation and preconditioning techniques which accelerate the inversion of the overlap operator by a factor of four on small lattices, with larger gains as the lattice size increases. These improvements can be used in both propagator calculations and dynamical simulations.

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arXiv2004

Numerical Methods for the QCD Overlap Operator: II. Optimal Krylov Subspace Methods

We investigate optimal choices for the (outer) iteration method to use when solving linear systems with Neuberger's overlap operator in QCD. Different formulations for this operator give rise to different iterative solvers, which are optimal for the respective formulation. We compare these methods in theory and practice to find the overall optimal one.For the first time, we apply the so-called SUMR method of Jagels and Reichel to the shifted unitary version of Neuberger's operator, and show that this method is in a sense the optimal choice for propagator computations. When solving the ``squared'' equations in a dynamical simulation with two degenerate flavours, it turns out that the CG method should be used.

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