Exact quantum ground state of a two-dimensional quasicrystalline antiferromagnet

Abstract

We present the exact dimer ground state of a quantum antiferromagnet defined on a quasicrystal constructed from the Bronze-mean hexagonal quasicrystal. A coupling isotropy on the first and second-neighbor bonds is sufficient to stabilize a product state of singlets on the third-neighbor bonds. We also provide a systematic approach for constructing additional crystals, quasicrystals, and amorphous structures that can sustain an exact dimer ground state.

7 pages, 6 figures

References in corpus (5)

• "Deconfined" quantum critical points
• Phase diagram of the Shastry-Sutherland Compound SrCu2(BO3)2 under extreme combined conditions of field and pressure
• Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-Al-Gd
• Another Exact Ground State of a 2D Quantum Antiferromagnet
• Fractalized magnon transport on the quasicrystal with enhanced stability

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• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Ferromagnetic Haldane state and dimer multiplet state of quantum ferromagnets
• Mott transition and correlation effects on strictly localized states in an octagonal quasicrystal
• Magnetization of Antiferromagnetic Cactus Graph Model with Exact Dimer Ground State
• Ground states of a family of frustrated spin models for quasicrystals and their approximants