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Cluster perturbation theory for electron-phonon systems

Cluster perturbation theory represents a powerful and versatile method to study spectral properties of strongly correlated systems. In existing work, the numerical diagonalization of the cluster problem has been done by means of the spectral decoding method which, however, faces problems due to numerical instabilities.

In this project, a recently developed kernel polynomial approach is applied to several open problems in the field of electron-phonon systems. To this end, we use high performance supercomputers and compute clusters.


The calculations consist of two steps.

  • The so-called cluster Green function is calculated on a finite system using open boundary conditions. This represents the numerically difficult part, and we use a MPI-based parallel code run on modern-day supercomputers (e.g., Hitachi SR800-F1 at the Externer Link:  LRZ) or compute clusters (e.g., CRAY strider opteron cluster at the Externer Link:  HLRS) with high-speed network connections. The dimensions of the sparse matrices in the matrix-vector multiplication are as large as 10 billion.
  • Once the moments of the single-particle Green function have been obtained, it is possible to compute the resulting spectral functions within a few seconds on a personal computer.

The final report of the Externer Link:  HPC-Europa project can be downloaded here: PDF: PDF-Datei: Report.


  • Dr. Martin Hohenadler
  • Dr. Gerhard Wellein
  • Prof. Dr. Holger Fehske (University Greifswald)
  • Dipl. Phys. Andreas Alvermann (University Greifswald)


  • M Hohenadler, G Wellein, A R Bishop, A Alvermann, and H Fehske, Spectral signatures of the Luttinger liquid to charge-density-wave transition, Phys. Rev. B 73, 245120 (2006).
  • H Fehske, A Alvermann, M Hohenadler, and G Wellein, Spectral signatures of Holstein polarons, Proc. Int. School of Physics ``Enrico Fermi'', Course CLXI, Polarons in Bulk Materials and Systems with Reduced Dimensionality, Eds. G. Iadonisi, J. Ranninger, G. de Filippis (IOS Press, Amsterdam, Oxford, Tokio, Washington DC, 2006), pp 285-296
  • J Loos, M Hohenadler, and H Fehske, Spectral functions of the spinless Holstein model, J. Phys.: Condens. Matter 18, 2453-2472 (2006)
  • G Wellein, A R Bishop, M Hohenadler, G Schubert, and H Fehske, Optical response of many-polaron systems, Physica B 378-380, 281-282 (2006)
  • M Hohenadler, G Wellein, A Alvermann, and H Fehske, Many-polaron problem by cluster perturbation theory, Physica B 378-380, 64-65 (2006)
  • M Hohenadler, D Neuber, W von der Linden, G Wellein, J Loos, and H Fehske, Photoemission spectra of many-polaron systems, Phys. Rev. B 71, 245111 (2005)


  • Talk: Cluster Perturbation Theory for electron-phonon systems, 27.07.2005, SCES'05, Vienna (AUT).
  • Poster: Photoemission spectra and optical response of many-polaron systems, presented at SCES'05, Vienna (AUT).
  • Poster: Photoemission spectra of many-polaron systems, Korrelationstage 2005, Dresden, Germany.


Logo des KONWIHR Projektes Logo des HPC-Europa Projektes This work is funded by Externer Link:  KONWIHR (Competence Network for Technical, Scientific High Performance Computing in Bavaria) and Externer Link:  HPC-Europa.

Letzte Änderung: 13. Maerz 2012, Historie

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