Distributions of Dirac operator eigenvalues

Akemann, Gernot; Damgaard, Poul H.

doi:10.1016/j.physletb.2003.12.024

Cited by 43 publications

(70 citation statements)

References 22 publications

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“…For µ > 1 the zeros are located on the real axis. Remarkably, the Yang-Lee zeros [58] of the model in [7] behave quite different from the model (20) discussed in this paper. The polynomials can also be interpreted as characteristic polynomials.…”

Section: B Partition Functions With One Flavorcontrasting

confidence: 65%

“…Below we will establish the nature of this singularity in the orthogonal polynomial approach. In fact, it does not enter in the calculation of the spectral density for the random matrix model (20) by means of complex orthogonal polynomials [34]. However, we will show that it occurs even at finite N in the random matrix model partition function with one bosonic quark and one conjugate bosonic quark of the same mass.…”

Section: Partition Function With Two Flavorsmentioning

confidence: 83%

“…In [34] it was shown that the partition function (20) has an eigenvalue representation after choosing an appropriate representation for the matrices Φ and Ψ yielding…”

Section: Random Matrix Model For Qcd At Nonzero Chemical Potentialmentioning

confidence: 99%

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Unquenched QCD Dirac operator spectra at nonzero baryon chemical potential

et al. 2005

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The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix model with the global symmetries of QCD. In this paper we show that these results and extensions thereof can be obtained from the replica limit of a Toda lattice equation. This naturally leads to a factorized form into bosonic and fermionic QCD-like partition functions. In the microscopic limit these partition functions are given by the static limit of a chiral Lagrangian that follows from the symmetry breaking pattern. In particular, we elucidate the role of the singularity of the bosonic partition function in the orthogonal polynomials approach. A detailed discussion of the spectral density for one and two flavors is given.

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Section: B Partition Functions With One Flavorcontrasting

confidence: 65%

Section: Partition Function With Two Flavorsmentioning

confidence: 83%

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Unquenched QCD Dirac operator spectra at nonzero baryon chemical potential

et al. 2005

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“…has not been proven so far, to our knowledge, that the single eigenvalue of the Dirac operator renormalizes with 1/Z S ; there are proposals on how to extract the distribution of the single eigenvalue directly from the chiral effective theory [60], but an explicit formula which includes sub-leading corrections has not been derived yet. Bearing in mind these caveats, it is interesting to notice that the values of Σ eff obtained in these computations are in good agreement with our result.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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“…In the broken phase at zero temperature and chemical potential the applicability of a matrix model has been completely understood by rederiving part of its results from the underlying effective chiral Lagrangian picture, that describes the pseudo-Goldstone fields. This has been achieved for the partition function [3], the spectral correlation functions of Dirac operator eigenvalues [4,5,6], as well as for individual eigenvalue correlations [7].…”

Section: Introductionmentioning

confidence: 99%

On matrix model partition functions for QCD with chemical potential

2004

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Partition functions of two different matrix models for QCD with chemical potential are computed for an arbitrary number of quark and complex conjugate anti-quark flavors. In the large-N limit of weak nonhermiticity complete agreement is found between the two models. This supports the universality of such fermionic partition functions, that is of products of characteristic polynomials in the complex plane. In the strong nonhermiticity limit agreement is found for an equal number of quark and conjugate flavours. For a general flavor content the equality of partition functions holds only for small chemical potential. The chiral phase transition is analyzed for an arbitrary number of quarks, where the free energy presents a discontinuity of first order at a critical chemical potential. In the case of nondegenerate flavors there is first order phase transition for each separate mass scale.

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Distributions of Dirac operator eigenvalues

Cited by 43 publications

References 22 publications

Unquenched QCD Dirac operator spectra at nonzero baryon chemical potential

Unquenched QCD Dirac operator spectra at nonzero baryon chemical potential

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

On matrix model partition functions for QCD with chemical potential

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