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A numerical study of the 2-flavour Schwinger model with dynamical overlap hypercube fermions

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Abstract

We present numerical results for the 2-flavour Schwinger model with dynamical chiral lattice fermions. We insert an approximately chiral hypercube Dirac operator into the overlap formula to construct the overlap hypercube operator. This is an exact solution to the Ginsparg–Wilson relation, with an excellent level of locality and scaling. Due to its similarity with the hypercubic kernel, a low polynomial in this kernel provides a numerically efficient Hybrid Monte Carlo force. We measure the microscopic Dirac spectrum and discuss the corresponding scale-invariant parameter, which takes a surprising form. This is an interesting case, since Random Matrix Theory is unexplored for this setting, where the chiral condensate Σ vanishes in the chiral limit. We also measure Σ and the “pion” mass, in distinct topological sectors. In this context we discuss and probe the topological summation of observables by various methods, as well as the evaluation of the topological susceptibility. The feasibility of this summation is essential for the prospects of dynamical overlap fermions in QCD.

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Authors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, C.P. 04510, Distrito Federal, Mexico

    Wolfgang Bietenholz

  2. Faculty of Geotechnical Engineering, University of Zagreb, Hallerova aleja 7, 42000, Varaždin, Croatia

    Ivan Hip

  3. Fakultät für Physik, Universität Bielefeld, 33615, Bielefeld, Germany

    Stanislav Shcheredin

  4. Potsdam Institute for Climate Impact Research, Telegrafenberg A62, 14412, Potsdam, Germany

    Jan Volkholz

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  1. Wolfgang Bietenholz
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  2. Ivan Hip
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Correspondence to Wolfgang Bietenholz.

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Bietenholz, W., Hip, I., Shcheredin, S. et al. A numerical study of the 2-flavour Schwinger model with dynamical overlap hypercube fermions. Eur. Phys. J. C 72, 1938 (2012). https://doi.org/10.1140/epjc/s10052-012-1938-9

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