Universal fluctuations in spectra of the lattice Dirac operator

Jan, 1995
11 pages
Published in:
  • Phys.Rev.Lett. 74 (1995) 3920-3923
e-Print:
Report number:
  • SUNY-NTG-95-3

Citations per year

19952002200920162023051015
Abstract: (arXiv)
Recently, Kalkreuter obtained the complete Dirac spectrum for an SU(2)SU(2) lattice gauge theory with dynamical staggered fermions on a 12412^4 lattice for β=1.8\beta =1.8 and β=2.8\beta=2.8. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble. In particular, long range fluctuations are strongly suppressed: the variance of a sequence of levels containing nn eigenvalues on average is given by Σ2(n)12π2(logn+const.)\Sigma_2(n) \sim\frac 1{2\pi^2}(\log n + {\rm const.}) instead of Σ2(n)=n\Sigma_2(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=2N_c=2 with staggered fermions which differs from the continuuum theory. For Nc=3N_c = 3 we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.
Note:
  • 8 pages + 3 figures (will be faxed on request)
  • gauge field theory: SU(2)
  • lattice field theory
  • operator: Dirac
  • spectrum: fluctuation
  • fluctuation: spectrum
  • correlation
  • statistical analysis
  • numerical calculations: Monte Carlo