About: Numerical analytic continuation

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In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies.

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  • In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies. Mathematically, the problem reduces to solving a Fredholm integral equation of the first kind with an ill-conditioned kernel. As a result, it is an ill-posed inverse problem with no unique solution and where a small noise on the input leads to large errors in the unregularized solution. There are different methods for solving this problem including the maximum entropy method, the average spectrum method and Pade approximation methods. (en)
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  • In many-body physics, the problem of analytic continuation is that of numerically extracting the spectral density of a Green function given its values on the imaginary axis. It is a necessary post-processing step for calculating dynamical properties of physical systems from quantum Monte Carlo simulations, which often compute Green function values only at imaginary-times or Matsubara frequencies. (en)
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  • Numerical analytic continuation (en)
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