The Bose-Glass Phase in Mean-Field Quasicrystalline Systems

We study the ground state phases of the Bose-Hubbard model with disordered potentials for quasicrystalline systems, with a focus on the Bose-Glass phase. Generally speaking, disorder can lead to the formation of a Bose-Glass, which is characterised by the lack of global phase coherence across the lattice. Here, we look at two models; the interacting 2D Aubry-Andre model and disordered quasicrystalline vertex models. Unlike typical disorder in homogeneous, periodic systems, quasicrystalline models possess self-similarity. This leads to a fascinating interplay between correlated, quasiperiodic order and uncorrelated, random disorder. In this work, we use a mean-field percolation analysis of superfluid clusters to map out the critical points and phase regions of these disordered systems. When the long-range order is separate to the random disorder, as is the case for the disordered vertex models, then the physics reflects that of periodic lattices with disorder. However, we find that long-range order present in the disorder term of the 2D Aubry-Andre model can result in some peculiarities to the physics of the Bose-Glass. This includes stabilisation from weak disorder lines and intricate, ordered structures of the phase itself that may provide fruitful areas of future study.