Exact quantum ground state of a two-dimensional quasicrystalline antiferromagnet

TL;DR

This paper demonstrates the exact ground state of a quantum antiferromagnet on a quasicrystal, revealing how specific couplings stabilize a singlet product state, and offers a method to construct similar structures with exact dimer ground states.

Contribution

It introduces an exact dimer ground state for a quasicrystalline antiferromagnet and a systematic approach for creating other structures with similar properties.

Findings

Exact dimer ground state on a quasicrystal

Coupling isotropy stabilizes singlet product state

Method for constructing structures with exact ground states

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.