  Symmetry protected topological (SPT) phases with gapless edge excitations
have been shown to exist in principle in strongly interacting bosonic/fermionic
systems and it is highly desirable to find practical systems to realize such
phases through numerical calculation. A central question to be addressed is how
to determine the SPT order in the system given the numerical simulation result
while no local order parameter can be measured to distinguish the phases from a
trivial one. In the tensor network approach to simulate strongly interacting
systems, the quantum state renormalization algorithm has been demonstrated to
be effective in identifying the intrinsic topological orders. Here we show that
a modified algorithm can identify SPT orders by extracting the fixed point
entanglement pattern in the ground state wave function which is essential for
the existence of SPT order. The key to this approach is to add symmetry
protection to the quantum state renormalization process and we demonstrate the
effectiveness of this algorithm with the example of AKLT states in both 1D and
2D.
