ar X iv : h ep - l at / 9 60 70 42 v 1 1 9 Ju l 1 99 6 1 Universal correlations in spectra of the lattice QCD Dirac operator
نویسندگان
چکیده
Recently, Kalkreuter obtained complete Dirac spectra for SU (2) lattice gauge theory both for staggered fermions and for Wilson fermions. The lattice size was as large as 12 4. We performed a statistical analysis of these data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal Ensemble for Wilson fermions. In both cases long range spectral fluctuations are strongly suppressed: the variance of a sequence of levels containing n eigenvalues on average is given by Σ2(n) ∼ 2(log n)/βπ 2 (β is equal to 4 and 1, respectively) instead of Σ2(n) = n for a random sequence of levels. Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for Nc = 2 with staggered fermions which differs from Wilson fermions (with the continuum anti-unitary symmetry). For Nc = 3, we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.
منابع مشابه
ar X iv : h ep - l at / 9 60 70 83 v 1 3 1 Ju l 1 99 6 1 ANL - HEP - CP - 96 - 55 CHIRAL QCD ( χ QCD ) ∗
Lattice QCD with staggered quarks is augmented by the addition of a chiral 4-fermion interaction. The Dirac operator is now non-singular at mq = 0, decreasing the computing requirements for light quark simulations by at least an order of magnitude. We present preliminary results from simulations at finite and zero temperatures for mq = 0, with and without gauge fields.
متن کاملar X iv : h ep - l at / 9 60 70 86 v 1 3 1 Ju l 1 99 6 1 Random matrix model approach to chiral symmetry
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for universal properties of the Dirac spectrum: i) finite volume corrections to valence quark mass dependence of the chiral condensate, and ii) microscopic fluctuatio...
متن کاملar X iv : h ep - l at / 9 60 70 27 v 1 1 0 Ju l 1 99 6
We implement lattice QCD using the Fortran 90 language. We have designed machine independent modules that define fields (gauge, fermions, scalars, etc...) and have defined overloaded operators for all possible operations between fields, matrices and numbers. With these modules it is very simple to write QCD programs. We have also created a useful compression standard for storing the lattice con...
متن کاملar X iv : h ep - l at / 9 91 00 40 v 1 2 5 O ct 1 99 9 RUHN - 99 - 3 The Overlap Dirac Operator ⋆
This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996