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Register a new userSparse modeling approach to obtaining the shear viscosity from smeared correlation functions
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We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method ($C(t,tau)$) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate that the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of $C(t,tau)$ only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed.
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We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation using Chebyshev polynomials. We test the method with numerical lattice data of Charmonium correlators. The method provides a framework to compare lattice calculation with experimental data including excited state contributions without assuming quark-hadron duality.
I derive an exact integral expression for the ratio of shear viscosity over entropy density $frac{eta}{s}$ for the massless (critical) O(N) model at large N with quartic interactions. The calculation is set up and performed entirely from the field theory side using a non-perturbative resummation scheme that captures all contributions to leading order in large N. In 2+1d, $frac{eta}{s}$ is evaluated numerically at all values of the coupling. For infinite coupling, I find $frac{eta}{s}simeq 0.42(1)times N$. I show that this strong coupling result for the viscosity is universal for a large class of interacting bosonic O(N) models.
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We consider the Schrodinger functional with staggered one-component fermions on a fine lattice of size $(L/a)^3 times (T/a)$ where $T/a$ must be an odd number. In order to reconstruct the four-component spinors, two different set-ups are proposed, corresponding to the coarse lattice having size $(L/2a)^3 times (T/2a)$, with $T = T pm a$. The continuum limit is then defined at fixed $T/L$. Both cases have previously been investigated in the pure gauge theory. Here we define fermionic correlation functions and study their approach to the continuum limit at tree-level of perturbation theory.
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