  In this paper we calculate the entanglement entropy of two coupled gapless
systems in general spatial dimension d. The gapless systems can be either
conformal field theories (CFT), or Fermi liquids. We assume the two systems are
coupled uniformly in a h-dimensional submanifold of the space, with 0 <= h <=
d. We will focus on the scaling of the entanglement entropy with the size of
the system, and its scaling with the inter-system coupling constant g. Three
approaches will be used for our calculation: (1) exact calculation with ground
state wave-functional, (2) perturbative calculation with functional path
integral, (3) scaling argument.
