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Time-dependent Gutzwiller approximation for the Hubbard model.

G Seibold1, J Lorenzana

  • 1Institut für Physik, Cottbus, Germany.

Physical Review Letters
|April 6, 2001
PubMed
Summary

We introduce a new time-dependent Gutzwiller approximation (GA) that improves upon traditional methods for the Hubbard model. This approach accurately predicts static and dynamic properties, offering better results than Hartree-Fock+random phase approximation (HF+RPA).

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Many-body theory

Background:

  • The Hubbard model is a fundamental model in condensed matter physics for understanding strongly correlated electron systems.
  • Accurate theoretical methods are crucial for describing the complex behavior of electrons in materials.

Purpose of the Study:

  • To develop a novel time-dependent Gutzwiller approximation (GA) for the Hubbard model.
  • To incorporate advanced correlation effects beyond the standard GA and Hartree-Fock+random phase approximation (HF+RPA) methods.
  • To evaluate the accuracy of the new formalism for both static and dynamic properties.

Main Methods:

  • Development of a time-dependent Gutzwiller approximation (GA) formalism.
  • Incorporation of ground-state correlations from the random phase approximation (RPA) into the GA.

Related Experiment Videos

  • Comparison of results with exact solutions in one dimension and with HF+RPA in two dimensions.

    • Main Results:

    • The new time-dependent GA shows excellent agreement with exact results for static quantities (ground state energy, double occupancy) in one dimension.
    • The method performs well across all coupling strengths in two dimensions for static properties.
    • Dynamical correlation functions computed using the new GA are significantly improved compared to HF+RPA and satisfy sum rules.

    Conclusions:

    • The developed time-dependent Gutzwiller approximation offers a substantial improvement over existing methods like HF+RPA for the Hubbard model.
    • This formalism provides a more accurate description of both static and dynamic correlations in strongly correlated systems.
    • The method's ability to reproduce exact results and satisfy sum rules highlights its potential for future studies in condensed matter physics.