Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

Akemann, Gernot; Bittner, Elmar

doi:10.1103/physrevlett.96.222002

Cited by 20 publications

(31 citation statements)

References 30 publications

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“…[4,11] and we will do that in a more systematic way. It is long known that the eigenvalue spectrum is informative in the vacuum [36] and the random matrix theory is capable of determining the low-lying spectrum, which has recently been extended to the finite density study [29,31,37]. Interestingly, the comparison to the random matrix model exhibits good agreement also in the case of the overlap fermion at µ = 0 [38].…”

Section: Introductionmentioning

confidence: 93%

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

Fukushima¹

2008

J. High Energy Phys.

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Abstract:We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential µ for a given gauge configuration on the finite-volume lattice. First, we elaborate the Banks-Casher relations in the complex plane extended for the diquark condensate as well as the chiral condensate to relate the eigenvalue spectral density to the physical observable. Next, we evaluate the condensates and clarify the characteristic spectral change corresponding to the phase transition. Assuming the strong coupling limit, we exhibit the numerical results for a random gauge configuration in two-color QCD implemented by the staggered fermion formalism and confirm that our results agree well with the known estimate quantitatively. We then exploit our method in the case of the Wilson fermion formalism with two flavors. Also we elucidate the possibility of the Aoki (parity-flavor broken) phase and conclude from the point of view of the spectral density that the artificial pion condensation is not induced by the density effect in strong-coupling two-color QCD.

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Section: Introductionmentioning

confidence: 93%

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

Fukushima¹

2008

J. High Energy Phys.

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“…Under this enlarged symmetry, composite mesons, baryons and anti-baryons occur in the same multiplets. A further consequence of pseudo-reality, is that the theory can be studied in the presence of non-zero quark chemical potential [10][11][12][13][14].…”

Section: The Lattice Calculationmentioning

confidence: 99%

Dark nuclei. II. Nuclear spectroscopy in two-color QCD

2014

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We consider two-colour QCD with two flavours of quarks as a possible theory of composite dark matter and use lattice field theory methods to investigate nuclear spectroscopy in the spin J = 0 and J = 1 multi-baryon sectors. We find compelling evidence that J = 1 systems with baryon number B = 2, 3 (and their mixed meson-baryon counterparts) are bound states -the analogues of nuclei in this theory. In addition, we estimate the σ-terms of the J = 0 and J = 1 single baryon states which are important for the coupling of the theory to scalar currents that may mediate interactions with the visible sector.

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“…Our surmise fills some gaps in predictions for real eigenvalues in the orthogonal and symplectic classes (β = 1, 4) [15], where until very recently numerically generated RMT had to be used for comparison [16]. We also provide new predictions for intermediate non-Hermiticity and test them against QCD-like LGT data from [17]. This further completes the picture, compared to previous approximations [14] (β = 2) based on a Fredholm determinant expansion [18], and exact results at maximal non-Hermiticity [19] (β = 2, 4).…”

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confidence: 99%

“…4 we compare to the 1st integrated eigenvalue, with α = 1.352 being close to maximal non-Hermiticity. No further fits compared to [17] are made. In Fig.…”

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Wigner surmise for Hermitian and non-Hermitian chiral random matrices

Akemann

Bittner²,

Phillips

et al. 2009

Phys. Rev. E

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We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit we find an excellent agreement, valid for a small number of exact zero-eigenvalues. New compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes, and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in Lattice Gauge Theory and we illustrate this by showing that our new results can describe data from two-colour QCD simulations with chemical potential in the symplectic class.PACS numbers: 02.10.Yn,12.38.Gc 1. Motivation. Probably one of the most used predictions of Random Matrix Theory (RMT) is the so-called Wigner surmise (WS) describing the universal repulsion of energy levels in many systems in nature, including neutron scattering, quantum billiards and elastomechanical modes in crystals [1]. For large matrices, the nearestneighbour (nn) spacing distribution p (β) (s) is universal and only depends on the repulsion strength which takes discrete values β = 1, 2, 4 for the three classical WignerDyson (WD) ensembles. It can be computed with surprising accuracy using 2 × 2 matrices, which is the WS. Although simple arguments discussed in [2] lead to this rule for β = 1, such an approximation is by no means obvious.The extension from WD to non-Hermitian RMT introduced long ago by Ginibre [3] has become a very active field in the past decade, in particular due to applications in open quantum systems, see [4] for references and other applications. Here the spacing is known only for the class with broken time-reversal (β = 2) and has been applied in Lattice Gauge Theory (LGT) [5]. However, a simple surmise based on 2 × 2 matrices does not work here.In this paper we investigate the existence of a surmise for the smallest eigenvalue in chiral RMT and its nonHermitian extensions. These have become relevant due to applications in Quantum Chromodynamics (QCD) initiated by [6] and extended to non-Hermitian QCD at finite quark chemical potential µ [7]. QCD at strong coupling is a notoriously difficult theory, and the chiral RMT approach has become an important tool for LGT with exact chiral fermions [8,9]. For non-Hermitian QCD the complex action hampers a straightforward LGT approach, see [10] for a recent discussion and references. Here RMT predictions remain possible for various quantities [11,12,13].In this paper we will show that an excellent approximation for the 1st non-zero eigenvalue is possible using a simple 2 × (2 + ν) matrix calculation, capturing the repulsion of a small number ν of zero eigenvalues. Being localised and non-oscillatory the 1st eigenvalue is much more suitable for LGT than the spectral density, compare e.g. [9] and [14]. Our surmise fills some gaps in predictions for real eigenvalues in the orthogonal and sympl...

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Unquenched Complex Dirac Spectra at Nonzero Chemical Potential: Two-Color QCD Lattice Data versus Matrix Model

Cited by 20 publications

References 30 publications

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD

Dark nuclei. II. Nuclear spectroscopy in two-color QCD

Wigner surmise for Hermitian and non-Hermitian chiral random matrices

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