We study the behavior of interacting ultracold bosons in optical lattices in synthetic magnetic fields with wide range of in-cell fluxes $\alpha =p/q$. The problem is similar to the one of an electron moving in a tight-binding scheme in the magnetic field and becomes difficult to tackle for a growing number of magnetic subbands, $q$. To overcome this, we focus on the interplay of the width, shape, and number of the subbands on the formation of the coherent state of cold bosons. Using the quantum rotor approach, which goes beyond the mean-field approximation, we are able to pinpoint the elements of the band structure, which are the most significant in a proper theoretical description of the synthetic magnetic field in a bosonic lattice system. As a result, we propose a method of reconstruction of the Hofstadter butterfly spectrum by replacing the magnetic subbands with renormalized bands of a square lattice. This allows us to effectively investigate the properties of the studied system for a wide range of magnetic fluxes and their impact on the Mott-insulator–superfluid transition.

• Received 24 November 2015

DOI:https://doi.org/10.1103/PhysRevA.93.053607