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@ARTICLE{Nghiem:874513,
      author       = {Nghiem, H. T. M. and Dang, H. T. and Costi, T. A.},
      title        = {{T}ime-dependent spectral functions of the {A}nderson
                      impurity model in response to a quench with application to
                      time-resolved photoemission spectroscopy},
      journal      = {Physical review / B},
      volume       = {101},
      number       = {11},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-01487},
      pages        = {115117},
      year         = {2020},
      abstract     = {We investigate several definitions of the time-dependent
                      spectral function A(ω,t) of the Anderson impurity model
                      following a quench and within the time-dependent numerical
                      renormalization group (TDNRG) method. In terms of the
                      single-particle two-time retarded Green function Gr(t1,t2),
                      the definitions we consider differ in the choice of the time
                      variable t with respect to t1 and/or t2 (which we refer to
                      as the time reference). In a previous study [H. T. M. Nghiem
                      et al., Phys. Rev. Lett. 119, 156601 (2017)], we
                      investigated the spectral function A(ω,t), obtained from
                      the Fourier transform of Im[Gr(t1,t2)] with respect to the
                      time difference t′=t1−t2, with time reference t=t2.
                      Here, we complement this work by deriving expressions for
                      the retarded Green function for the choices t=t1 and the
                      average, or Wigner, time t=(t1+t2)/2, within the TDNRG
                      approach. We compare and contrast the resulting A(ω,t) for
                      the different choices of time reference. While the choice
                      t=t1 results in a spectral function with no time dependence
                      before the quench (t<0) (being identical to the equilibrium
                      initial-state spectral function for t<0), the choices
                      t=(t1+t2)/2 and t=t2 exhibit nontrivial time evolution both
                      before and after the quench. Expressions for the lesser,
                      greater, and advanced Green functions are also derived
                      within TDNRG for all choices of time reference. The
                      average-time lesser Green function G<(ω,t) is particularly
                      interesting, as it determines the time-dependent occupied
                      density of states N(ω,t)=G<(ω,t)/(2πi), a quantity that
                      determines the photoemission current in the context of
                      time-resolved pump-probe photoemission spectroscopy. We
                      present calculations for N(ω,t) for the Anderson model
                      following a quench, and discuss the resulting time evolution
                      of the spectral features, such as the Kondo resonance and
                      high-energy satellite peaks. We also discuss the issue of
                      thermalization at long times for N(ω,t). Finally, we use
                      the results for N(ω,t) to calculate the time-resolved
                      photoemission current for the Anderson model following a
                      quench (acting as the pump) and study the different
                      behaviors that can be observed for different resolution
                      times of a Gaussian probe pulse.},
      cin          = {IAS-3},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-3-20090406},
      pnm          = {142 - Controlling Spin-Based Phenomena (POF3-142)},
      pid          = {G:(DE-HGF)POF3-142},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000518950200002},
      doi          = {10.1103/PhysRevB.101.115117},
      url          = {https://juser.fz-juelich.de/record/874513},
}