Bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns.

The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field antiferromagnetic (AFM) patterns is theoretically studied. We report on a specific tight-binding model of artificial AFM structures incorporating both nearest and next-to-nearest neighbour tunnelings and allowing for the formation of the fractal spectra even with the vanishing gauge field flux through the lattice. The model is applied to square and honeycomb lattices. Possible experimental realization is suggested for the lattices of microring resonators connected by waveguides. Finally, the structure of the butterflies is analyzed for different points in the magnetic Brillouin zone for both the ferromagnetic and AFM patterns.