What are topological phases of matter? First, they are phases of matter at
zero temperature. Second, they have a non-zero energy gap for the excitations
above the ground state. Third, they are disordered liquids that seem have no
feature. But those disordered liquids actually can have rich patterns of
many-body entanglement representing new kinds of order. This paper will give a
simple introduction and a brief survey of topological phases of matter. We will
first discuss topological phases that have topological order (ie with long
range entanglement). Then we will cover topological phases that have no
topological order (ie with only short-range entanglement).Comment: 18 pages, 8 figures, 4 tables. A short review, expanded versio
