Two-dimensional entanglement entropy with chemical potential and topological Wilson loops

We compute the entanglement and Renyi entropies for Dirac fermions on a 2 dimensional torus in the presence of chemical potential, current source, and topological Wilson loops. These gauge fields are unified in a single framework by exhausting all the ingredients of the electromagnetic vertex operators of the Z_n orbifold conformal field theory.
Our analytic computations reveal numerous novelties. The following two key findings resolve the existing unsettled issues. (1) On a circle, the entropies subtly depend on the chemical potential in the zero temperature limit, which is useful for probing the ground state energy levels of quantum systems. (2) In the infinite space limit, these entropies become exact and depend only on the topological Wilson loops. We provide an organizing tool for various topological phase transitions for the entropies and show that entanglement entropy is non-singular and continuous across the topological sectors.