Entanglement entropy in (2+1)-dimensional quantum field theories*

We develop a method to calculate the entanglement entropy for (2+1)D quantum field theories, by representing the 3D replicated Green's function in term of an infinite series of the connected diagrams in 2D replica space-time manifold. Within this framework, an exact derivation of the area-law entanglement entropy for (2+1)D free scalar and Dirac fields is provided. Moreover, our method guides a perturbative approach to interacting theories, by considering the interaction as a correction to the 2D replicated two-point function. Especially, our method allows an explicit calculation of the entanglement entropy in disordered system. We discuss the case of a (2+1)D Dirac filed under a static random gauge field as a concrete example. The corresponding lattice simulation gives consistent results with our analytical solution, indicates the ability of our method to capture ultraviolet behaviors of entanglement entropy in generic interacting field theories.