For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this idea on fermionic systems. Why? Is the reason that for the spin systems, the total hilbert space is a tensor product of the hilbert spaces of each spin, while for identical fermions, the total hilbert has not such a tensor product structure?