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Ladder operator for the one-dimensional Hubbard model.

J Links1, H Q Zhou, R H McKenzie

  • 1Centre for Mathematical Physics, School of Physical Sciences, The University of Queensland, Brisbane 4072, Australia.

Physical Review Letters
|June 1, 2001
PubMed
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We constructed a ladder operator to generate conserved currents for the one-dimensional Hubbard model. This method applies to Yang-Baxter integrable systems, differing from Lorentz-invariant models.

Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Mathematical physics

Background:

  • The one-dimensional Hubbard model is a fundamental model in condensed matter physics.
  • Integrable models possess an infinite number of conserved quantities, simplifying their analysis.
  • Lorentz invariance is a key property in many physical systems, but not all.

Purpose of the Study:

  • To explicitly construct a ladder operator for the one-dimensional Hubbard model.
  • To demonstrate a novel method for generating conserved currents.
  • To highlight the differences in construction compared to Lorentz-invariant systems.

Main Methods:

  • Construction of a ladder operator using a general formalism.
  • Iterative generation of conserved current operators.

Related Experiment Videos

  • Application of methods derived from solutions to the Yang-Baxter equation.

    • Main Results:

    • An explicit construction of a ladder operator for the one-dimensional Hubbard model was achieved.
    • This operator allows for the iterative generation of all conserved current operators.
    • The construction method is distinct from those used for Lorentz-invariant systems.

    Conclusions:

    • The developed ladder operator formalism provides a powerful tool for studying integrable systems.
    • The method is applicable to a broad class of models derived from the Yang-Baxter equation.
    • The non-Lorentz invariant nature of the Hubbard model necessitates unique construction techniques.