Exact quantum ground state of a two-dimensional quasicrystalline antiferromagnet

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