Can someone please let me know if there is some reference for the calculation of entanglement entropy of $U(1)$ lattice gauge theory? I have seen a few references where Z2 lattice gauge theory has been dealt with. Also these references suggest that since in a lattice gauge theory the degrees of freedom live on links hence the Hilbert space of states can't be decomposed into a direct product of states belonging entirely to a region, say A and its complement B because of links which cross the boundary of the region of interest.
My question is can I not gauge fix the link variables crossing the boundary of the region of interest so that link variables belonging solely to the complement region can be traced over unambiguously to obtain the reduced density matrix.
Also how do I write down a gauge invariant ground state wave function for a U(1) lattice gauge theory in order to define the density matrix?