Haldane phase and magnetic ordering in the spin-$1$ anisotropic bilinear-biquadratic system on the square lattice

ORAL

Abstract

To investigate possible symmetry protected topological Haldane phase in two dimensions, we study a spin-$1$ bilinear-biquadratic model on the square lattice with spacing anisotropic interactions by combining analytic analysis and density matrix renormalization group. In the absence of interchain couplings, the system reduces to the decoupled Haldane chains when the biquadratic coupling $K_x$ ($K_x > 0$) is smaller than the bilinear coupling $J_x$ ($J_x > 0$). By switching on the interchain couplings $J_y, K_y$ with fixed coupling ratio $K_x/J_x = K_y/J_y$, we find that for $K_x/J_x \lesssim 0.5$, the Haldane phase of the decoupled chains extends to finite interchain couplings with $J_y$ up to about $0.4$,
and is followed by a phase transition to a N\'eel magnetic order. For $K_x/J_x \gtrsim 0.5$, the Haldane phase appears fragile in the presence of interchain couplings and we find a magnetic order for weak interchain interactions. Our results indicate that although the inclusion of biquadratic interaction extends the Haldane phase regime, it is still limited in small interchain couplings.

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Presenters

  • Shoushu Gong

    Department of Physics, Beihang University, Beihang University, National High Magnetic Field Laboratory

Authors

  • Shoushu Gong

    Department of Physics, Beihang University, Beihang University, National High Magnetic Field Laboratory

  • Wenjun Hu

    Department of Physics and Astronomy, Rice University, Rice Univ, Department of Physics and Astronomy, Rice Univ

  • Hsin-Hua Lai

    Department of Physics and Astronomy, Rice University, Rice Univ, Physics and Astronomy, and Rice Center for Quantum Materials, Rice University, Department of Physics and Astronomy, Rice Univ

  • Andriy Nevidomskyy

    Department of Physics and Astronomy, Rice University, Physics and Astronomy, Rice University, Department of Physics and Astronomy, Rice Univ, Rice University

  • Qimiao Si

    Department of Physics and Astronomy, Rice University, Physics and Astronomy, Rice Univ, Physics and Astronomy, Rice University, Rice Univ, Rice Universiry, Physics, Rice University, Rice University, Department of Physics and Astronomy and Rice Center for Quantum Materials, Rice University, Physics and Astronomy, and Rice Center for Quantum Materials, Rice University, Department of Physics and Astronomy, Rice Univ

  • Kun Yang

    Department of Physics, National High Magnetic Field Laboratory and Florida State University, National High Magnetic Field Laboratory, Florida State University