p band in a rotating optical lattice

We investigate the effects of rotation on the excited bands of a tight-binding lattice, focusing particularly on the first excited (p) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a nontrivial splitting and magnetic fine structure of the p band. We show that Peierls substitution can be modified to describe p band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first-principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p band can be investigated starting from this effective Hamiltonian.