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.