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Register a new userProgress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
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Authors
K. Splittorff
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Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wilson Dirac operator in the $epsilon$-domain of QCD with dynamical quarks. We have also obtained the distribution of the chiralities over the real eigenvalues of the Wilson Dirac operator for any number of flavors. All results have been derived for a fixed index of the Dirac operator. An important effect of dynamical quarks is that they completely suppress the inverse square root singularity in the spectral density of the Hermitian Wilson Dirac operator. The analytical results are given in terms of an integral over a diffusion kernel for which the square of the lattice spacing plays the role of time. This approach greatly simplifies the expressions which we here reduce to the evaluation of two-dimensional integrals.
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QCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a controlled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed N_t approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly.
QCD is investigated at finite temperature using Wilson fermions in the fixed scale approach. A 2+1 flavor stout and clover improved action is used at four lattice spacings allowing for control over discretization errors. The light quark masses in this first study are fixed to heavier than physical values. The renormalized chiral condensate, quark number susceptibility and the Polyakov loop is measured and the results are compared with the staggered formulation in the fixed N_t approach. The Wilson results at the finest lattice spacing agree with the staggered results at the highest N_t.
The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Greens functions, which apply both on-shell and off-shell.
We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number. The spectrum in the entire eigenvalue range is obtained with a single set of measurements. Results on 2+1-flavor ensembles with Mobius domain-wall sea quarks at lattice spacing ~ 0.08 fm are shown.
We compute the overlap Dirac spectrum on three ensembles generated using 2+1 flavor domain wall fermions. The spectral density is determined up to $lambdasim$100 MeV with sub-percentage statistical uncertainty. The three ensembles have different lattice spacings and two of them have quark masses tuned to the physical point. We show that we can resolve the flavor content of the sea quarks and constrain their masses using the Dirac spectral density. We find that the density is close to a constant below $lambdale$ 20 MeV (but 10% higher than that in the 2-flavor chiral limit) as predicted by chiral perturbative theory ($chi$PT), and then increases linearly due to the strange quark mass. Using the next to leading order $chi$PT, one can extract the light and strange quark masses with $sim$20% uncertainties. Using the non-perturbative RI/MOM renormalization, we obtain the chiral condensates at $overline{textrm{MS}}$ 2 GeV as $Sigma=(260.3(0.7)(1.3)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=2$ (keeping the strange quark mass at the physical point) chiral limit and $Sigma_0=(232.6(0.9)(1.2)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=3$ chiral limit, where the four uncertainties come from the statistical fluctuation, renormalization constant, continuum extrapolation and lattice spacing determination. Note that {$Sigma/Sigma_0=1.40(2)(2)$ is much larger than 1} due to the strange quark mass effect.
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