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Related Experiment Videos

Schwinger-Keldysh semionic approach for quantum spin systems.

M N Kiselev1, R Oppermann

  • 1Institut für Theoretische Physik, Universität Würzburg, D-97074 Würzburg, Germany.

Physical Review Letters
|January 3, 2001
PubMed
Summary

We developed a new path-integral Schwinger-Keldysh approach for quantum spin systems using a semionic representation. This method exactly accounts for local constraints, simplifying diagram techniques for models like the Heisenberg model.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Many-Body Physics

Background:

  • Quantum spin systems are crucial in condensed matter physics.
  • Existing representations like Holstein-Primakoff and Dyson-Maleev have limitations in handling local constraints.
  • Developing efficient theoretical frameworks is essential for understanding complex magnetic phenomena.

Purpose of the Study:

  • To derive a novel path-integral Schwinger-Keldysh approach for quantum spin systems.
  • To introduce a semionic representation of spins as fermions with imaginary chemical potential.
  • To establish a simplified diagrammatic technique that exactly incorporates local constraints.

Main Methods:

  • Utilizing a semionic representation of spins.
  • Employing an imaginary chemical potential for fermions.

Related Experiment Videos

  • Developing a path-integral formulation within the Schwinger-Keldysh formalism.
  • Applying the standard Feynman diagram technique.

    • Main Results:

    • A new path-integral Schwinger-Keldysh approach for quantum spin systems is derived.
    • The semionic representation allows for exact treatment of local constraints.
    • A standard diagram technique with Feynman rules is established.
    • The approach is demonstrated on the Heisenberg model for Néel and spin-liquid states.

    Conclusions:

    • The derived approach offers a significant simplification compared to other representations.
    • This method provides an exact and efficient tool for studying quantum spin systems.
    • The technique is applicable to various magnetic phases, including Néel and spin-liquid states.