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Anyonic Haldane Insulator in One Dimension.

Florian Lange1,2, Satoshi Ejima2, Holger Fehske2

  • 1Computational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan.

Physical Review Letters
|April 8, 2017
PubMed
Summary

We numerically show a topological Haldane phase in a 1D extended Hubbard model for bosons and anyons. This phase, protected by symmetries, offers potential for experimental verification via dynamical structure factor asymmetry.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Topological Phases of Matter

Background:

  • The extended Hubbard model describes interacting particles on a lattice.
  • Topological phases exhibit unique properties robust against local perturbations.
  • Haldane phases are a specific type of topological phase with potential applications.

Purpose of the Study:

  • To numerically demonstrate the existence of a topological Haldane phase in the 1D extended Hubbard model.
  • To investigate this phase for both bosons and anyons.
  • To identify conditions and methods for experimental verification.

Main Methods:

  • Numerical simulations using a matrix-product-state based infinite density-matrix renormalization group (iDMRG) scheme.
  • Analysis of generalized transfer matrices to verify topological protection.

Related Experiment Videos

  • Calculation of the dynamical density structure factor.

    • Main Results:

    • Existence of a nontrivial topological Haldane phase confirmed for bosons and anyons at one particle per site.
    • The Haldane insulator phase is identified within the V-U parameter plane, adjacent to superfluid, Mott insulator, and density-wave phases.
    • The phase is shown to be protected by combined spatial-inversion and time-reversal symmetries.

    Conclusions:

    • A topological Haldane phase exists in the 1D extended Hubbard model for both bosons and anyons.
    • This phase is robust and protected by specific symmetries, even with broken reflection parity.
    • The asymmetry of the dynamical density structure factor is proposed as a key experimental signature for the anyonic Haldane insulator.