Interacting bosons on crystalline and quasiperiodic ladders in a magnetic field

We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field, and crystalline or quasiperiodic geometries. Motion will be induced on charged particles when a magnetic field is present, which can result in exotic distributions of current on a lattice. Typically, the geometry of a ladder lattice is assumed to be homogeneous. In this paper, however, we will study superlattice and quasicrystalline ladders that possess nonuniform bond lengths, in order to study the formation of localized currents. By using density matrix renormalization group (DMRG) to characterize the quantum phases, we confirm the presence of the usual vortex and Meissner distributions of current, in which particles circulate within the bulk and around the edge respectively. Furthermore, it is also possible to observe variations to these patterns; which combine both vortex and Meissner order, and the onset of incompressible domains for specific fillings of the lattice. If the bond lengths of a ladder fluctuate, we find substantial differences to the structure of currents. This is a consequence of an inhomogeneous, effective magnetic flux, resulting in preferential localization of currents throughout the lattice bulk, towards the smaller bond lengths. We then find that incompressible domains can significantly grow in size extent across the parameter space, with currents no longer possessing an extended structure across the longitudinal direction of the ladder.