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Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension.

S Anders1, M B Plenio, W Dür

  • 1Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria.

Physical Review Letters
|October 10, 2006
PubMed
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We developed a new variational method using weighted graph states to approximate ground states in strongly interacting spin systems. This approach efficiently computes observables and handles complex entanglement, applicable to various dimensions and models.

Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Strongly interacting spin systems present significant challenges for traditional computational methods.
  • Approximating ground states is crucial for understanding material properties and quantum phenomena.
  • Existing methods often struggle with arbitrary geometries, high dimensions, and complex entanglement.

Purpose of the Study:

  • Introduce a novel variational method for approximating ground states of strongly interacting spin systems.
  • Develop a technique applicable to diverse geometries and spatial dimensions.
  • Enable efficient computation of local observables and characterization of entanglement properties.

Main Methods:

  • Utilize weighted graph states and their superpositions as variational wavefunctions.

Related Experiment Videos

  • Implement the method for the Ising model on 1D, 2D, and 3D square lattices.
  • Generalize the approach to higher spins and continuous-variable systems.

    • Main Results:

    • The method efficiently computes local observables, including energy, for strongly interacting spin systems.
    • The weighted graph states capture states with diverging correlation lengths and unbounded multiparticle entanglement.
    • Successful application to Ising models across various dimensions demonstrates the method's versatility.

    Conclusions:

    • The proposed variational method offers a powerful tool for studying complex quantum many-body systems.
    • This approach facilitates the investigation of lattice field theories and systems with significant entanglement.
    • The technique provides a pathway to explore ground states in arbitrary geometries and dimensions.