Level spacing distribution of critical random matrix ensembles

Nishigaki, Shinsuke M.

doi:10.1103/physreve.58.r6915

Cited by 20 publications

(25 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To focus more closely on just the smallest eigenvalue, we have also compared its distribution with the analytical predictions for different topological sectors [15]. Let us denote the distribution of the lowest (rescaled) eigenvalue in a sector of topological charge ν by P (ν) (ζ).…”

Section: The Microscopic Dirac Operator Spectrummentioning

confidence: 99%

Staggered fermions and gauge field topology

Damgaard¹,

Heller

Niclasen³

et al. 1999

Phys. Rev. D

View full text Add to dashboard Cite

Based on a large number of smearing steps, we classify SU͑3͒ gauge field configurations in different topological sectors. For each sector we compare the exact analytical predictions for the microscopic Dirac operator spectrum of quenched staggered fermions. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero, showing explicitly that the smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are insensitive to gauge field topology. On the smeared configurations, 4 eigenvalues clearly separate out from the rest on configurations of topological charge , and move towards zero in agreement with the index theorem.

show abstract

Section: The Microscopic Dirac Operator Spectrummentioning

confidence: 99%

Staggered fermions and gauge field topology

Damgaard¹,

Heller

Niclasen³

et al. 1999

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…Entrusting that these universality among three different ensembles [34] to be an indication of uniqueness of multifractal deformation of the classical random matrices, one of the authors (SMN) computed the LSDs of Ensemble I in three symmetry classes [35,36] (Fig.3). Ensemble I is…”

Section: Pos(lattice 2013)018mentioning

confidence: 99%

“…For e.g. the unitary class, the LSD is expressed as P β =2 (s) = ∂ 2 s e − ∫ s 0 dtR(t) in terms of the diagonal resolvent R(t) = t|K a (I − K a ) −1 |t , which satisfies a transcendental equation of Painlevé VI type [35],…”

Section: Pos(lattice 2013)018mentioning

confidence: 99%

Critical statistics at the mobility edge of QCD Dirac spectra

Nishigaki¹,

Giordano²,

Kovács³

et al. 2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

View full text Add to dashboard Cite

We examine statistical fluctuation of eigenvalues from the near-edge bulk of QCD Dirac spectra above the critical temperature. For completeness we start by reviewing on the spectral property of Anderson tight-binding Hamiltonians as described by nonlinear σ models and random matrices, and on the scale-invariant intermediate spectral statistics at the mobility edge. By fitting the level spacing distributions, deformed random matrix ensembles which model multifractality of the wave functions typical of the Anderson localization transition, are shown to provide an excellent effective description for such a critical statistics. Next we carry over the above strategy for the Anderson Hamiltonians to the Dirac spectra. For the staggered Dirac operators of QCD with 2+1 flavors of dynamical quarks at the physical point and of SU(2) quenched gauge theory, we identify the precise location of the mobility edge as the scaleinvariant fixed point of the level spacing distribution. The eigenvalues around the mobility edge are shown to obey critical statistics described by the aforementioned deformed random matrix ensembles of unitary and symplectic classes. The best-fitting deformation parameter for QCD at the physical point turns out to be consistent with the Anderson Hamiltonian in the unitary class. Finally, we propose a method of locating the mobility edge at the origin of QCD Dirac spectrum around the critical temperature, by the use of individual eigenvalue distributions of deformed chiral random matrices.

show abstract

“…The correlation functions of the latter model have been derived by means of q-orthogonal polynomials [45,46] and Painlevé equations [47]. In this paper we are interested in chiral random matrix ensembles defined as ensembles of N × N random matrices with the structure…”

Section: Definition Of the Modelmentioning

confidence: 99%

Chiral random matrix model for critical statistics

García-García

Verbaarschot

2000

Nuclear Physics B

View full text Add to dashboard Cite

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a noninteracting Fermi-gas we show that for energy differences less than a critical energy E c the spectral correlations are given by chiral Random Matrix Theory whereas for energy differences larger than E c the number variance shows a linear dependence on the energy difference with a slope that depends on the parameters of the model. If the parameters are scaled such that the slope remains fixed in the thermodynamic limit, this model provides a description of QCD Dirac spectra in the universality class of critical statistics. In this way a good description of QCD Dirac spectra for gauge field configurations given by a liquid of instantons is obtained.

show abstract

Level spacing distribution of critical random matrix ensembles

Cited by 20 publications

References 30 publications

Staggered fermions and gauge field topology

Staggered fermions and gauge field topology

Critical statistics at the mobility edge of QCD Dirac spectra

Chiral random matrix model for critical statistics

Contact Info

Product

Resources

About