  In this four-part prospectus, we first give a brief introduction to the
motivation for studying entanglement entropy and some recent development. Then
follows a summary of our recent work about entanglement entropy in states with
traditional long-range order. After that we demonstrate calculation of
entanglement entropy in both one-dimensional spin-less fermionic systems as
well as bosonic systems via different approaches, and connect them using
one-dimensional bosonization. In the last part, we briefly sketch the idea of
bosonization in high-dimensions, and discuss the possibility and advantage of
approaching the scaling behavior of entanglement entropy of fermions in
arbitrary dimensions via bosonization.
