  We propose a type of phase transition in quantum many-body systems, which
occurs in highly excited quantum many-body scar states, while the rest of the
spectrum is largely unaffected. Such scar state phase transitions can be
realized by embedding a matrix product state, known to undergo a phase
transition, as a scar state into the thermal spectrum of a parent Hamiltonian.
We find numerically that the mechanism for the scar state phase transition
involves the formation or presence of low-entropy states at energies similar to
the scar state in the vicinity of the phase transition point.
