4.6 Article

Excitations and spectra from equilibrium real-time Green?s functions

期刊

PHYSICAL REVIEW B
卷 106, 期 12, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.106.125153

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资金

  1. U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) programme [DE-SC0022088]
  2. European Research Council (ERC) under the European Union [854843-FASTCORR]
  3. Swedish National Infrastructure [SNIC 2020/5-698, SNIC 2020/6-294]
  4. Swedish Research Council [2018-05973]
  5. U.S. Department of Energy (DOE) [DE-SC0022088] Funding Source: U.S. Department of Energy (DOE)

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The paper proposes a real-time discretization method based on a piecewise high-order orthogonal-polynomial expansion to address the storage requirements of Green's function and the computational cost of solving the Dyson equation. By using a compact high-order discretization and specific algorithms, long-time simulations can be performed with fewer discretization points.
The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this paper, we apply a real-time discretization based on a piecewise high-order orthogonal-polynomial expansion to address these issues. We present a superconvergent algorithm for solving the real-time equilibrium Dyson equation using the Legendre spectral method and the recursive algorithm for Legendre convolution. We show that the compact high-order discretization in combination with our Dyson solver enables long-time simulations using far fewer discretization points than needed in conventional multistep methods. As a proof of concept, we compute the molecular spectral functions of H2, LiH, He2, and C6H4O2 using self-consistent second-order perturbation theory and compare the results with standard quantum chemistry methods as well as the auxiliary second-order Green's function perturbation theory method.

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