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Hubbard model on decorated lattices.

C D Batista1, B S Shastry

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|October 4, 2003
PubMed
Summary
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Researchers developed new lattices enabling quasiexact solutions for the Hubbard model. The ground state on a decorated Kagomè lattice features local currents, described by an S=1/2 XY model.

Area of Science:

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

Background:

  • The Hubbard model is a fundamental model in condensed matter physics describing interacting electrons in solids.
  • Solving the Hubbard model exactly is notoriously difficult due to its complexity.
  • Quasiexact solutions offer valuable insights into the ground and low-energy states of quantum systems.

Purpose of the Study:

  • To introduce a novel family of lattices that allow for quasiexact solutions of the Hubbard model.
  • To rigorously determine the ground state properties of the Hubbard model on a decorated Kagomè lattice.
  • To develop a low-energy effective theory for the emergent chiral state.

Main Methods:

  • Development of a specific lattice structure amenable to analytical solutions.

Related Experiment Videos

  • Rigorous mathematical treatment of the Hubbard model Hamiltonian on the decorated Kagomè lattice.
  • Derivation of the low-energy effective field theory.

    • Main Results:

    • A family of lattices enabling quasiexact solvability for the Hubbard model and its extensions.
    • Identification of the ground state on the decorated Kagomè lattice as an ordered array of local currents.
    • The low-energy description of this chiral state is an S=1/2 XY model.

    Conclusions:

    • The introduced lattices provide a powerful tool for studying interacting electron systems.
    • The decorated Kagomè lattice hosts a novel chiral ground state with potential applications in quantum magnetism.
    • The S=1/2 XY model effectively captures the low-energy physics of this emergent state.