Spectrum of the Wilson Dirac operator at finite lattice spacings

Akemann, Gernot; Damgaard, Poul H.; Splittorff, K.; Verbaarschot, J. J. M.

doi:10.1103/physrevd.83.085014

Cited by 70 publications

(225 citation statements)

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“…[7], differs in sign from that used in Refs. [5,6]. 2 Since these LECs appear at leading order in the appropriate power-counting, they are independent of the renormalization scale.…”

Section: Introductionmentioning

confidence: 99%

“…A further method of constraining LECs has recently been discovered in the context of calculating the lowenergy spectrum and eigenvalue properties of the lattice Hermitian Wilson-Dirac operator [5,6]. One line of argument is based on the positivity of the underlying two-flavor fermion determinant, which follows from the γ 5 −hermiticity of the Wilson-Dirac operator.…”

Section: Introductionmentioning

confidence: 99%

“…One line of argument is based on the positivity of the underlying two-flavor fermion determinant, which follows from the γ 5 −hermiticity of the Wilson-Dirac operator. Specif-ically, the partition function at fixed (odd) topology is positive in the underlying theory but is only positive in the effective theory (here partially quenched Wilson ChPT [PQWChPT]) if the LECs satisfy a constraint [6]. In the standard convention for LECs, 1 this constraint…”

Section: Introductionmentioning

confidence: 99%

“…[5,6,9] imply an interesting corollary if one assumes that scaling at large N c (number of colors) is a good guide at N c = 3. In particular, since 1 Note that our convention for W ′ j , which follows Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Another line of argument notes that the partially-quenched partition function for zero-momentum modes (which determines the leading order behavior in the ǫ-regime) converges only if [5,6]. 3 We also note that a similar constraint (specifically, W ′ 8 ≤ 0 independent of W ′ 6 and W ′ 7 ) was found earlier by one of us, based on the finding that the method for calculating the spectral density in infinite volume using PQWChPT only worked if the constraint held [9].…”

Section: Introductionmentioning

confidence: 99%

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Constraint on the low energy constants of Wilson chiral perturbation theory

Hansen

Sharpe

2012

Phys. Rev. D

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Wilson chiral perturbation theory (WChPT) is the effective field theory describing the longdistance properties of lattice QCD with Wilson or twisted-mass fermions. We consider here WChPT for the theory with two light flavors of Wilson fermions or a single light twisted-mass fermion. Discretization errors introduce three low energy constants (LECs) into partially quenched WChPT at O(a 2 ), conventionally called W ′ 6 , W ′ 7 and W ′ 8 . The phase structure of the theory at non-zero a depends on the sign of the combination 2W ′ 6 + W ′ 8 , while the spectrum of the lattice Hermitian Wilson-Dirac operator depends on all three constants. It has been argued, based on the positivity of partition functions of fixed topological charge, and on the convergence of graded group integrals that arise in the ǫ-regime of ChPT, that there is a constraint on the LECs arising from the underlying lattice theory. In particular, for W ′ 6 = W ′ 7 = 0, the constraint found is W ′ 8 ≤ 0. Here we provide an alternative line of argument, based on mass inequalities for the underlying partially quenched theory. We find that W ′ 8 ≤ 0, irrespective of the values of W ′ 6 and W ′ 7 . Our constraint implies that 2W ′ 6 > |W ′ 8 | if the phase diagram is to be described by the first-order scenario, as recent simulations suggest is the case for some choices of action.

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“…[7], differs in sign from that used in Refs. [5,6]. 2 Since these LECs appear at leading order in the appropriate power-counting, they are independent of the renormalization scale.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constraint on the low energy constants of Wilson chiral perturbation theory

Hansen

Sharpe

2012

Phys. Rev. D

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Complex Langevin simulation of a random matrix model at nonzero chemical potential

Bloch

Glesaaen

Verbaarschot

et al. 2018

J. High Energ. Phys.

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In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.

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Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

Necco

Shindler

2011

J. High Energ. Phys.

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Abstract:We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass m and the lattice spacing a obey the relative power counting m ∼ aΛ 2 QCD : in this situation discretisation effects can be treated as perturbation of the continuum behaviour. While this framework fails to describe lattice spectral density close to the threshold, it allows nevertheless to investigate important properties of the spectrum of the Wilson Dirac operator. We discuss the range of validity of our results and the possible implications in understanding the phase diagram of Wilson fermions.

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Spectrum of the Wilson Dirac operator at finite lattice spacings

Abstract: We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac

Cited by 70 publications

References 70 publications

Constraint on the low energy constants of Wilson chiral perturbation theory

Constraint on the low energy constants of Wilson chiral perturbation theory

Complex Langevin simulation of a random matrix model at nonzero chemical potential

Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

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