The Mean-Field Bose Glass in Quasicrystalline Systems

Abstract

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 will look at two models; the interacting 2D Aubry-Andre model and disordered vertex models from quasicrystalline tiling patterns. 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 combine Gutzwiller mean-field theory with a percolation analysis of superfluid clusters, allowing the critical points and phase regions of these disordered systems to be mapped. When the longrange 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. These peculiarities include stabilisation from weak disorder lines and intricate, ordered structures of the phase itself that may provide fruitful areas of future study.

Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity

“…Another interesting question is how the BLT states would appear or alter the physics in the presence of interactions. The study of the physics of two-dimensional quasicrystals including interactions is an emergent topic [96][97][98]. With the recent advances in many-body numerical techniques [99][100][101], the physics of BLT states and their ramifications in quasicrystalline lattices in the many-body regime could soon be probed.…”

Finite-temperature phases of trapped bosons in a two-dimensional quasiperiodic potential

“…Recently, a number of studies have investigated the properties of interacting bosons in two-dimensional quasicrystalline potentials on quasicrystalline lattices in continuous space [19], in the tight-binding limit [20], and on a square lattice through the 2D Aubry-André model [21,22]. Some of these works have delineated phase diagrams in the mean-field approximation, and for strongly interacting particles; they have shown that regions of BG appear between the superfluid (SF) and Mott insulator (MI) phases, similarly to the disordered case.…”

Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice

“…The existence of a BG and the regime of strong interactions remain, however, largely unexplored. On the theoretical side, mean field phase diagrams have been found using inhomogeneous Gutzwiller-like ansatz on simplified quasiperiodic graphs [53][54][55]. Such approaches, however, ignore beyond-mean field effects in the vicinity of critical points as well as the exact connectivity of optical qua-sicrystals.…”