N. Cundy - Academia.edu (original) (raw)
Papers by N. Cundy
Computer Physics Communications, 2008
ABSTRACT We present preliminary results of a test of our dynamical overlap simulations, where we ... more ABSTRACT We present preliminary results of a test of our dynamical overlap simulations, where we calculate the unrenormalized chiral condensate from a direct calculation, the overlap eigenvalue distribution and the topological susceptibility. We observe a (as yet) unrenormalized chiral condensate of −(2493(18) MeV), with good agreement between the various methods.
Physics Letters B, 2012
We investigate how the topological charge density in lattice QCD simulations is affected by viola... more We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new m... more 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.
V. G. Bornyakov, 3 P. V. Buividovich, N. Cundy, O. A. Kochetkov, 2, ∗ and A. Schäfer Institute fo... more V. G. Bornyakov, 3 P. V. Buividovich, N. Cundy, O. A. Kochetkov, 2, ∗ and A. Schäfer Institute for High Energy Physics, 142281, Protvino, Russia Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia Far Eastern Federal University, Sukhanova Street 8, Vladivostok 690950, Russia Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Lattice Gauge Theory Research Center, FPRD, and CTP Department of Physics and Astronomy, Seoul National University,Seoul, 151-747, South Korea (Dated: August 15th, 2014)
We study the influence of an external magnetic field on the deconfinement transition in twoflavou... more We study the influence of an external magnetic field on the deconfinement transition in twoflavour 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 6 lattice and at a pion mass around 500 MeV. The pion mass (as well as the lattice spacing) was determined in independent runs on 12 3 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 [3].
Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005), 2005
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
We have reported elsewhere in this conference on our continuing project to determine nonperturbat... more We have reported elsewhere in this conference on our continuing project to determine nonperturbative 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 Landaugauge 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.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is a... more 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 overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
J µ J ν £ (where J is the vector current) and comparing it with the expectation values of bilinea... more J µ J ν £ (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 ¥ 2xF 1. We use overlap fermions because of their improved chiral properties, which reduces the number of possible operator mixing coefficients.
Journal of Physics: Conference Series, 2011
The δ-regime of QCD is characterised by light quarks in a small spatial box, but a large extent i... more The δ-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 δ-expansion-applies, based on a quantum mechanical treatment of the quasi onedimensional system. In particular, for vanishing quark masses one obtains a residual pion mass M R π , which has been computed to the third order in the δ-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 δ-regime. This is very tedious, but results compatible with the predictions for M R π have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the δ-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constantl3.
Computer Physics Communications, 2009
Tunnelling between different topological sectors with dynamical chiral fermions is difficult beca... more Tunnelling between different topological sectors with dynamical chiral fermions is difficult because of a poor mass scaling of the pseudo-fermion estimate of the determinant. For small fermion masses it is virtually impossible using standard methods. However, by projecting out the small Wilson eigenvectors from the overlap operator, and treating the correction determinant exactly, we can significantly increase the rate of topological sector tunnelling and reduce substantially the auto-correlation time. We present and compare a number of different approaches, and advocate a method which allows topological tunnelling even at low mass with little addition to the computational cost.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
QCD results are presented for a 2+1 flavour fermion clover action (which we call the SLiNC action... more 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.
Lecture Notes in Computational Science and Engineering, 2005
We investigate optimal choices for the (outer) iteration method to use when solving linear system... more 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.
Physics Letters B, 2014
We investigate the relationship between colour confinement and topological structures derived fro... more We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho-Duan-Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field n which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson Loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension.
Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, 2006
We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a me... more We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a method which can be used to account for the delta function in the fermionic force caused by the differential of the sign function. We discuss the algoritmic difficulties that have been overcome, and mention those that still need to be solved.
Physical Review D, 2014
We study the influence of an external magnetic field on the deconfinement transition in twoflavou... more We study the influence of an external magnetic field on the deconfinement transition in twoflavour 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 ×6 lattice and at a pion mass around 500 MeV. The pion mass (as well as the lattice spacing) was determned in the independent runs on 12 3 × 24 lattices. We consider two temperatures, one of which is close to the deconfinement transition and the other is above it. 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.
Nuclear Physics B - Proceedings Supplements, 2005
We present relaxation and preconditioning techniques which accelerate the inversion of the overla... more 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.
Computer Physics Communications, 2008
ABSTRACT We present preliminary results of a test of our dynamical overlap simulations, where we ... more ABSTRACT We present preliminary results of a test of our dynamical overlap simulations, where we calculate the unrenormalized chiral condensate from a direct calculation, the overlap eigenvalue distribution and the topological susceptibility. We observe a (as yet) unrenormalized chiral condensate of −(2493(18) MeV), with good agreement between the various methods.
Physics Letters B, 2012
We investigate how the topological charge density in lattice QCD simulations is affected by viola... more We investigate how the topological charge density in lattice QCD simulations is affected by violations of chiral symmetry caused by the fermion action. To this end we compare lattice configurations generated with a number of different actions including first configurations generated with exact dynamical overlap quarks. We visualize the topological profiles after mild smearing. In the topological charge correlator we measure the size of the positive core, which is known to shrink to zero extension in the continuum limit. To leading order we find the core size to scale linearly with the lattice spacing with the same coefficient for all actions, even including quenched simulations. In the subleading term the different actions vary over a range of about 10%. Our findings suggest that non-chiral lattice actions at current lattice spacings do not differ much for observables related to topology, both among themselves and compared to overlap fermions.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new m... more 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.
V. G. Bornyakov, 3 P. V. Buividovich, N. Cundy, O. A. Kochetkov, 2, ∗ and A. Schäfer Institute fo... more V. G. Bornyakov, 3 P. V. Buividovich, N. Cundy, O. A. Kochetkov, 2, ∗ and A. Schäfer Institute for High Energy Physics, 142281, Protvino, Russia Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia Far Eastern Federal University, Sukhanova Street 8, Vladivostok 690950, Russia Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany Lattice Gauge Theory Research Center, FPRD, and CTP Department of Physics and Astronomy, Seoul National University,Seoul, 151-747, South Korea (Dated: August 15th, 2014)
We study the influence of an external magnetic field on the deconfinement transition in twoflavou... more We study the influence of an external magnetic field on the deconfinement transition in twoflavour 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 6 lattice and at a pion mass around 500 MeV. The pion mass (as well as the lattice spacing) was determined in independent runs on 12 3 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 [3].
Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005), 2005
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
We have reported elsewhere in this conference on our continuing project to determine nonperturbat... more We have reported elsewhere in this conference on our continuing project to determine nonperturbative 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 Landaugauge 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.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is a... more 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 overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition.
Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008
J µ J ν £ (where J is the vector current) and comparing it with the expectation values of bilinea... more J µ J ν £ (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 ¥ 2xF 1. We use overlap fermions because of their improved chiral properties, which reduces the number of possible operator mixing coefficients.
Journal of Physics: Conference Series, 2011
The δ-regime of QCD is characterised by light quarks in a small spatial box, but a large extent i... more The δ-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 δ-expansion-applies, based on a quantum mechanical treatment of the quasi onedimensional system. In particular, for vanishing quark masses one obtains a residual pion mass M R π , which has been computed to the third order in the δ-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 δ-regime. This is very tedious, but results compatible with the predictions for M R π have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the δ-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constantl3.
Computer Physics Communications, 2009
Tunnelling between different topological sectors with dynamical chiral fermions is difficult beca... more Tunnelling between different topological sectors with dynamical chiral fermions is difficult because of a poor mass scaling of the pseudo-fermion estimate of the determinant. For small fermion masses it is virtually impossible using standard methods. However, by projecting out the small Wilson eigenvectors from the overlap operator, and treating the correction determinant exactly, we can significantly increase the rate of topological sector tunnelling and reduce substantially the auto-correlation time. We present and compare a number of different approaches, and advocate a method which allows topological tunnelling even at low mass with little addition to the computational cost.
Proceedings of The XXVII International Symposium on Lattice Field Theory — PoS(LAT2009), 2010
QCD results are presented for a 2+1 flavour fermion clover action (which we call the SLiNC action... more 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.
Lecture Notes in Computational Science and Engineering, 2005
We investigate optimal choices for the (outer) iteration method to use when solving linear system... more 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.
Physics Letters B, 2014
We investigate the relationship between colour confinement and topological structures derived fro... more We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho-Duan-Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field n which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson Loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension.
Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, 2006
We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a me... more We discuss the adaptation of the Hybrid Monte Carlo algorithm to overlap fermions. We derive a method which can be used to account for the delta function in the fermionic force caused by the differential of the sign function. We discuss the algoritmic difficulties that have been overcome, and mention those that still need to be solved.
Physical Review D, 2014
We study the influence of an external magnetic field on the deconfinement transition in twoflavou... more We study the influence of an external magnetic field on the deconfinement transition in twoflavour 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 ×6 lattice and at a pion mass around 500 MeV. The pion mass (as well as the lattice spacing) was determned in the independent runs on 12 3 × 24 lattices. We consider two temperatures, one of which is close to the deconfinement transition and the other is above it. 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.
Nuclear Physics B - Proceedings Supplements, 2005
We present relaxation and preconditioning techniques which accelerate the inversion of the overla... more 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.