Phason-disordered two-dimensional quantum antiferromagnets

We examine a type of disorder that is unusual in the context of quantum antiferromagnets although well known in the literature of quasiperiodic systems. Our model consists of localized spins with antiferromagnetic exchanges on a bipartite quasiperiodic structure, which is geometrically disordered in such a way that no frustration is introduced. In the limit of zero disorder, the structure is the perfect Penrose rhombus tiling. This tiling is progressively disordered by augmenting the number of random “phason flips” or local tile-reshuffling operations. The ground state remains Néel ordered, and we have studied its properties as a function of increasing disorder using linear spin-wave theory and quantum Monte Carlo. We find that the ground-state energy decreases, indicating enhanced quantum fluctuations with increasing disorder. The magnon spectrum is progressively smoothed, and the effective spin-wave velocity of low-energy magnons increases with disorder. For large disorder, the ground-state energy as well as the average staggered magnetization tend toward limiting values characteristic of this type of randomized tilings.