Scattering approach to the entanglement entropy area law for fermions

The entanglement entropy (EE) of a critical fermion system coupled to another system by a ``weak link'' is studied perturbatively in the weak link amplitude, $w$. In this model, EE arises from $s$-wave scattering connecting the two subsystems and is computed from perturbative corrections to the subsystem correlation function. The first non-vanishing contribution to the EE, appearing at $O(w^2)$, may be evaluated analytically and is shown to diverge as $w^2 \ln^2{L}$, where $L$ is the linear subsystem size. A generalized version of this model containing many independent weak links is discussed in connection with the entropy area law for fermions.