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@ARTICLE{Merker:22463,
      author       = {Merker, L. and Costi, T.A.},
      title        = {{N}umerical renormalization group calculation of impurity
                      internal energy and specific heat of quantum impurity
                      models},
      journal      = {Physical review / B},
      volume       = {86},
      number       = {7},
      issn         = {1098-0121},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-22463},
      pages        = {075150},
      year         = {2012},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {We introduce a method to obtain the specific heat of
                      quantum impurity models via a direct calculation of the
                      impurity internal energy requiring only the evaluation of
                      local quantities within a single numerical renormalization
                      group (NRG) calculation for the total system. For the
                      Anderson impurity model we show that the impurity internal
                      energy can be expressed as a sum of purely local static
                      correlation functions and a term that involves also the
                      impurity Green function. The temperature dependence of the
                      latter can be neglected in many cases, thereby allowing the
                      impurity specific heat C-imp to be calculated accurately
                      from local static correlation functions; specifically via
                      C-imp = partial derivative E-ionic/partial derivative T +
                      1/2 partial derivative E-hyb/partial derivative T, where
                      E-ionic and E-hyb are the energies of the (embedded)
                      impurity and the hybridization energy, respectively. The
                      term involving the Green function can also be evaluated in
                      cases where its temperature dependence is non-negligible,
                      adding an extra term to C-imp. For the nondegenerate
                      Anderson impurity model, we show by comparison with exact
                      Bethe ansatz calculations that the results recover
                      accurately both the Kondo induced peak in the specific heat
                      at low temperatures as well as the high-temperature peak due
                      to the resonant level. The approach applies to multiorbital
                      and multichannel Anderson impurity models with arbitrary
                      local Coulomb interactions. An application to the Ohmic
                      two-state system and the anisotropic Kondo model is also
                      given, with comparisons to Bethe ansatz calculations. The
                      approach could also be of interest within other impurity
                      solvers, for example, within quantum Monte Carlo
                      techniques.},
      keywords     = {J (WoSType)},
      cin          = {PGI-2 / IAS-3},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106 / I:(DE-Juel1)IAS-3-20090406},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Physics, Condensed Matter},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000308004600002},
      doi          = {10.1103/PhysRevB.86.075150},
      url          = {https://juser.fz-juelich.de/record/22463},
}