  Some quantum critical states cannot be smoothly deformed into each other
without either crossing some multicritical points or explicitly breaking
certain symmetries even if they belong to the same universality class. This
brings up the notion of ``symmetry-enriched'' quantum criticality. While recent
works in the literature focused on critical states with robust degenerate edge
modes, we propose that the conformal boundary condition (b.c.) is a more
generic characteristic of such quantum critical states. We show that in two
families of quantum spin chains, which generalize the Ising and the three-state
Potts models, the quantum critical point between a symmetry-protected
topological phase and a symmetry-breaking order realizes a conformal b.c.
distinct from the simple Ising and Potts chains. Furthermore, we argue that the
conformal b.c. can be derived from the bulk effective field theory, which
realizes a novel bulk-boundary correspondence in symmetry-enriched quantum
critical states.
