A new method to measure the chiral condensate in lattice QCD using Wilson fermions

Bitar, Khalil M.; Heller, Urs M.; Narayanan, Rajamani

doi:10.1016/s0370-2693(97)01487-1

Cited by 29 publications

(46 citation statements)

References 8 publications

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“…Moreover, the Aoki phase manifests itself in the smallest eigenvalues of the Wilson Dirac operator [11,40]. Here we show that the behavior of the smallest eigenvalues of the Wilson Dirac operator is also directly related to the Sharpe-Singleton scenario.…”

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confidence: 53%

Realization of the Sharpe-Singleton scenario

2012

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The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a 2 corrections of the chiral Lagrangian in the microscopic limit. The result is used to demonstrate how the Sharpe-Singleton first order scenario is realized in terms of the eigenvalues of the Wilson Dirac operator. We show that the Sharpe-Singleton scenario only takes place in the theory with dynamical fermions whereas the Aoki phase can be realized in the quenched as well as the unquenched theory. Moreover, we give constraints imposed by γ 5 -Hermiticity on the additional low energy constants of Wilson chiral perturbation theory.

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confidence: 53%

Realization of the Sharpe-Singleton scenario

2012

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“…Based on this continuum result, Ref. [6] argues that, if the spectrum of γ 5 W (m 0 ) has no gap, then one should interpret the lattice theory as having massless quarks and chiral symmetry breaking.…”

Section: B the Proposal Of Bitar Heller And Narayananmentioning

confidence: 99%

“…[17] and adopted also in Refs. [6][7][8]. § Spectral densities can be defined on a given gauge configuration by taking the infinite volume limit.…”

Section: B the Proposal Of Bitar Heller And Narayananmentioning

confidence: 99%

Spontaneous flavor and parity breaking with Wilson fermions

1998

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We discuss the phase diagram of Wilson fermions in the m 0 -g 2 plane for twoflavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken "Aoki phase". We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width ∆m 0 ∼ a 3 with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order a. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.UW/PT 98-2 hep-lat/9804028Typeset in LaT E X †

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“…Since small Dirac eigenvalues are very sensitive to the index, ν, of the Dirac operator we will work at fixed ν. This index is determined from the spectral flow of the eigenvalues of D 5 (m) [22,23] (see Fig. 1).…”

Section: Pos(lattice 2011)113mentioning

confidence: 99%

Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions

Splittorff¹,

Verbaarschot²

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wilson Dirac operator in the ε-domain of QCD with dynamical quarks. We have also obtained the distribution of the chiralities over the real eigenvalues of the Wilson Dirac operator for any number of flavors. All results have been derived for a fixed index of the Dirac operator. An important effect of dynamical quarks is that they completely suppress the inverse square root singularity in the spectral density of the Hermitian Wilson Dirac operator. The analytical results are given in terms of an integral over a diffusion kernel for which the square of the lattice spacing plays the role of time. This approach greatly simplifies the expressions which we here reduce to the evaluation of two-dimensional integrals.

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A new method to measure the chiral condensate in lattice QCD using Wilson fermions

Abstract: Parity and flavor symmetry is not broken in QCD. Using this fact, we propose a new method to measure the chiral condensate in lattice QCD using Wilson fermions with an operator that breaks parity and flavor in addition to the chiral symmetry.

Cited by 29 publications

References 8 publications

Realization of the Sharpe-Singleton scenario

Realization of the Sharpe-Singleton scenario

Spontaneous flavor and parity breaking with Wilson fermions

Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions

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