I am trying to understand the presence of complex hopping amplitudes in Hubbard-like lattice models. The hopping term features the so called "Peierls phase": $$ - t\sum_{j=1}^L \left( c_{j+1}^\dagger c_{j} e^{+i\frac{\Phi}{L}} + c_{j}^\dagger c_{j+1}e^{-i\frac{\Phi}{L}} \right) $$ where $L$ is the number of lattice sites and periodic boundary conditions are assumed, meaning that $j=L+1 \equiv 1$. Hence, we are dealing with a ring lattice.
In Literature, I have read that this hopping terms is what you get if the ring is rotated with angular frequency $\Omega$ , upon transforming from the laboratory frame into the rotating frame. In the latter frame, there is Coriolis force, which is analogous to having a magnetic flux $\Phi=2 \pi m R^2\Omega/\hbar$ through the ring.
I would like to understand why a rotation is formally equivalent to the presence of a magnetic flux. More specifically: if this magnetic flux $\Phi$ is constant in time, the associated electric field $\vec{E}=-\partial\vec{A}/\partial t$ should be zero, and so there shouldn't be any driving force acting tangentially.
