Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
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DOI：
10.1007/jhep07(2020)007
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发表时间：
2020-04
影响因子：
5.4
通讯作者：
E. Itou;Y. Nagai
中科院分区：
文献类型：
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作者：
E. Itou;Y. Nagai
我们提出了一种稀疏建模方法来估计拖尾相关函数的谱函数。我们描述了如何从有限温度下猝灭的QCD的重整化能量动量张量的关联函数(C(t，τ))中得到切变粘度。梯度流法中的重整化EMT的测量由于其涂抹的性质而减少了统计不确定度。然而，拖尾破坏了谱函数的求和规则，相关函数中的过度拖尾数据可能不得不从物理观测数据的分析过程中剔除。在这项工作中，我们演示了连接松原频率数据和真实频率数据的中间表示基(IR基)的稀疏建模分析。即使仅在梯度流的基准窗口中使用非常有限的C(t，τ)数据，该方法也能很好地工作。我们利用ADMM算法来解决某些约束条件下的套索问题。我们证明了所得到的谱函数在有限的流时间重现了输入的拖尾相关函数。文中还讨论了几种系统误差和统计误差以及流量与时间的关系。
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, τ)) 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 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, τ) 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.