  Two gapped quantum ground states in the same phase are connected by an
adiabatic evolution which gives rise to a local unitary transformation that
maps between the states. On the other hand, gapped ground states remain within
the same phase under local unitary transformations. Therefore, local unitary
transformations define an equivalence relation and the equivalence classes are
the universality classes that define the different phases for gapped quantum
systems. Since local unitary transformations can remove local entanglement, the
above equivalence/universality classes correspond to pattern of long range
entanglement, which is the essence of topological order. The local unitary
transformation also allows us to define a wave function renormalization scheme,
under which a wave function can flow to a simpler one within the same
equivalence/universality class. Using such a setup, we find conditions on the
possible fixed-point wave functions where the local unitary transformations
have \emph{finite} dimensions. The solutions of the conditions allow us to
classify this type of topological orders, which generalize the string-net
classification of topological orders. We also describe an algorithm of wave
function renormalization induced by local unitary transformations. The
algorithm allows us to calculate the flow of tensor-product wave functions
which are not at the fixed points. This will allow us to calculate topological
orders as well as symmetry breaking orders in a generic tensor-product state.
