Towards the chiral limit with dynamical blocked Wilson fermions

Barbour, I.M.; Laermann, Edwin; Lippert, Thomas; Schilling, Klaus

doi:10.1103/physrevd.46.3618

Cited by 15 publications

(43 citation statements)

References 24 publications

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“…Unfortunately, for the unchanged, non-hermitian Wilson-Dirac matrix M (or Q respectively) the situation is less suitable for the Lanczos method without reorthogonalization. Barbour et al [9,35] report that they were not able to compute all the eigenvalues and they were forced to reorthogonalize. In that case, the Lanczos vectors have to be stored and storage requirements become comparable with standard methods.…”

Section: Diagonalization Of Q and Checksmentioning

confidence: 99%

On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

Gattringer

Hip

1998

Nuclear Physics B

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We study characteristic features of the eigenvalues of the WilsonDirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors with real eigenvalues as the lattice equivalents of the continuum zero-modes. We demonstrate, that those properties of the spectrum which correspond to non-trivial topology are stable under adding fluctuations to the gauge fields. The behavior of the spectrum in a fully quantized theory is discussed using QED 2 as an example.

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Section: Diagonalization Of Q and Checksmentioning

confidence: 99%

On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

Gattringer

Hip

1998

Nuclear Physics B

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“…and therefore can be used as an indicator for approaching the chiral limit (see, e.g., [8,14]). However, it is generally not known for which classes of distributions of eigenvalues eq.…”

Section: Action and Observablesmentioning

confidence: 99%

“…In fact, very close to the transition point κ ≃ κ c (β) such configurations appear to be very 'normal' (see, e.g. [7,8,9,10]). In practice the appearance of these configurations can be used as an indicator for approaching κ c (β).…”

Section: Introductionmentioning

confidence: 99%

On the chiral limit in lattice gauge theories with Wilson fermions

Hoferichter

Mitrjushkin

Müller–Preussker

1997

Zeitschrift f�r Physik C Particles and Fields

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The chiral limit κ ≃ κ c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimatorm π for the calculation of the pseudoscalar mass m π is proposed which does not suffer from 'divergent' contributions at κ ≃ κ c (β). We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play no physical role. The behaviour of the subtracted chiral condensate ψψ subt near κ c (β) is determined. We observe a comparatively large value of ψψ subt · Z −1 P , which could be interpreted as a possible effect of the quenched approximation.

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“…Note that the Schur complement can be used to obtain effective fermions such as used in the blocked fermion approach to full QCD [53].…”

Section: Renormalization Group and Projective Multigridmentioning

confidence: 99%

Algebraic multigrid operators for disordered systems and lattice gauge theory

Best¹

2001

AIP Conference Proceedings

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The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the effective coarse-grid operator is obtained as the Schur complement of the original matrix. An optimal approximation to it is found by a numerical optimization procedure akin to Monte Carlo renormalization, resulting in a generalized (gauge-path dependent) stencil that is easily evaluated for a given disorder field. Applications to preconditioning and relaxation methods are investigated. * Electronic address: c.best@computer.org 1 Contents

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Towards the chiral limit with dynamical blocked Wilson fermions

Cited by 15 publications

References 24 publications

On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

On the spectrum of the Wilson-Dirac lattice operator in topologically non-trivial background configurations

On the chiral limit in lattice gauge theories with Wilson fermions

Algebraic multigrid operators for disordered systems and lattice gauge theory

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