  Symmetry fractionalization, generating a large amount of symmetry-protected
topological phases, provides scenarios for continuous phase transitions
different from spontaneous symmetry breaking. However, it is hard to detect
these symmetry-protected topological phase transitions experimentally.
Motivated by the recent development of highly tunable ultracold polar
molecules, we show that the setup in a zigzag optical lattice of this system
provides a perfect platform to realize symmetry-protected topological phase
transitions. By using infinite time-evolving block decimation, we obtain the
phase diagram in a large parameter regions and find another scheme to realize
the long-sought vector chiral phase, which is robust from quantum fluctuations.
We discuss the existence of the chiral phase by an effective field analysis.
