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@ARTICLE{Nghiem:902441,
      author       = {Nghiem, H. T. M. and Costi, Theodoulos},
      title        = {{S}elf-energy method for time-dependent spectral functions
                      of the {A}nderson impurity model within the time-dependent
                      numerical renormalization group approach},
      journal      = {Physical review / B},
      volume       = {104},
      number       = {20},
      issn         = {1098-0121},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2021-04263},
      pages        = {205113},
      year         = {2021},
      abstract     = {The self-energy method for quantum impurity models
                      expresses the correlation part of the self-energy in terms
                      of the ratio of two Green's functions and allows for a more
                      accurate calculation of equilibrium spectral functions than
                      is possible directly from the one-particle Green's function
                      [Bulla et al., J. Phys.: Condens. Matter 10, 8365 (1998)],
                      for example, within the numerical renormalization group
                      method. In addition, the self-energy itself is a central
                      quantity required in the dynamical mean field theory of
                      strongly correlated lattice models. Here, we show how to
                      generalize the self-energy method to the time-dependent
                      situation for the prototype model of strong correlations,
                      the Anderson impurity model. We use the equation-of-motion
                      method to obtain closed expressions for the local Green's
                      function in terms of a time-dependent correlation
                      self-energy, with the latter being given as a ratio of a
                      one-particle time-dependent Green's function and a
                      higher-order correlation function. We benchmark this
                      self-energy approach to time-dependent spectral functions
                      against the direct approach within the time-dependent
                      numerical renormalization group method. The self-energy
                      approach improves the accuracy of time-dependent spectral
                      function calculations, and the closed-form expressions for
                      the Green's function allow for a clear picture of the time
                      evolution of spectral features at the different
                      characteristic time scales. The self-energy approach is of
                      potential interest also for other quantum impurity solvers
                      for real-time evolution, including time-dependent density
                      matrix renormalization group and continuous-time quantum
                      Monte Carlo techniques.},
      cin          = {IAS-3},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-3-20090406},
      pnm          = {5213 - Quantum Nanoscience (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5213},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000719865400004},
      doi          = {10.1103/PhysRevB.104.205113},
      url          = {https://juser.fz-juelich.de/record/902441},
}