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Green's function of a dressed particle.

Mona Berciu1

  • 1Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada.

Physical Review Letters
|August 16, 2006
PubMed
Summary

This study introduces an efficient and accurate method for approximating Green's functions of dressed particles, like the Holstein polaron. The new technique improves accuracy across various coupling strengths, offering a valuable tool for condensed matter physics research.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory
  • Solid State Physics

Background:

  • Approximating Green's functions is crucial for understanding the behavior of interacting quantum systems.
  • Existing methods, such as the self-consistent Born approximation, often rely on summing specific subclasses of diagrams, limiting their accuracy.
  • The Holstein polaron model serves as a standard test case for developing and validating new theoretical approaches.

Purpose of the Study:

  • To develop a novel, highly efficient, and accurate approximation for the Green's functions of dressed particles.
  • To apply and validate this new method using the Holstein polaron model.
  • To assess the accuracy and applicability of the proposed approximation across a wide range of coupling strengths.

Main Methods:

  • The proposed method involves summing all self-energy diagrams, rather than a subclass.
  • Each diagram is averaged over its free propagators' momenta.
  • This approach is demonstrated using the Holstein polaron model.

Main Results:

  • The new Green's function approximation exactly satisfies the first six spectral weight sum rules.
  • Higher-order spectral weight sum rules are satisfied with high accuracy.
  • The approximation becomes asymptotically exact for both very weak and very strong coupling regimes relative to the free particle bandwidth.

Conclusions:

  • The developed approximation offers a significant improvement in both efficiency and accuracy for calculating Green's functions of dressed particles.
  • The method shows excellent performance for the Holstein polaron model, suggesting potential for broader applicability.
  • Further generalizations to other quantum many-body models are feasible and warrant investigation.

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