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@ARTICLE{Mankodi:1035359,
      author       = {Mankodi, Ishan N. H. and DiVincenzo, David P.},
      title        = {{P}erturbative power series for block diagonalisation of
                      {H}ermitian matrices},
      reportid     = {FZJ-2025-00406, arXiv:2408.14637},
      year         = {2025},
      note         = {7 pages, 1 figure},
      abstract     = {Block diagonalisation of matrices by canonical
                      transformation is important in various fields of physics.
                      Such diagonalization is currently of interest in condensed
                      matter physics, for modelling of gates in superconducting
                      circuits and for studying isolated quantum many-body
                      systems. While the block diagonalisation of a particular
                      Hermitian matrix is not unique, it can be made unique with
                      certain auxiliary conditions. It has been assumed in some
                      recent literature that two of these conditions, ``least
                      action' vs. block-off-diagonality of the generator, lead to
                      identical transformations. We show that this is not the
                      case, and that these two approaches diverge at third order
                      in the small parameter. We derive the perturbative power
                      series of the ``least action', exhibiting explicitly the
                      loss of block-off-diagnoality.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2408.14637},
      howpublished = {arXiv:2408.14637},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2408.14637;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1035359},
}