Interacting Bosons on Crystalline and Quasiperiodic Ladders in a Magnetic Field

TL;DR

This paper investigates how interactions, magnetic fields, and lattice geometries, including quasiperiodic structures, influence current patterns and quantum phases in ladder systems using DMRG simulations.

Contribution

It introduces the study of non-uniform bond length ladders and their impact on current localization and quantum phases in Hofstadter ladder models.

Findings

Standard vortex and Meissner current patterns are confirmed.

Inhomogeneous bond lengths cause localized currents and larger incompressible domains.

Currents tend to localize around smaller bond lengths due to effective magnetic flux variations.

Abstract

We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field and crystalline or quasiperiodic geometries. Rotational 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 work, however, we will also study ladders that possess non-uniform bond lengths, in order to study the formation of localised currents. By using Density Matrix Renormalisation Group (DMRG) to characterise 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 certain 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 localisation 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.