Entanglement Entropy, Chemical Potential, Current Source, and Wilson Loop

We construct and analytically compute entanglement and the R\'enyi entropies of Dirac fermions on a 2 dimensional torus in the presence of background chemical potential, current source and Wilson loop, by employing correlation functions of the electromagnetic vertex operators of $\mathbb{Z}_n$ orbifold theory. The entropies reveal numerous novelties. They probe the energy levels of compact fermions through the chemical potential, demonstrate interference phenomena with the current source being `beat frequency,' and experience topological phase transitions by dialing the Wilson loop, in the low temperature limit. In the large radius limit, they depend only on the Wilson loop via topological transitions, which are tightly linked to conformal dimension of the electromagnetic operators.