Phason Disorder Effects in the Penrose Tiling Antiferromagnet

We discuss the ground state of a disordered two dimensional Heisenberg antiferromagnet. The starting structure is taken to be a perfectly deterministic quasiperiodic tiling, and the type of disorder we consider is geometric, involving frozen phason flips of a randomly selected subset of sites. We consider S=1/2 quantum spins placed on the vertices of the tiling, and interacting with the nearest neighbor spins with a uniform exchange interaction J. We calculate the energy spectrum, ground state energy and real space local magnetization values as a function of degree of disorder. We find that quantum fluctuations are enhanced by disorder. The real space staggered magnetization loses its symmetry properties and the average staggered magnetization decreases compared to the case of the perfect Penrose tiling. We explain our results in terms of a simple Heisenberg star cluster model that takes into account the changes of local environments due to phason flips.