The existence of degenerated ground states of a many-body quantum system is usually taken as a signature of the quantum order.
I am considering the follow question:
If we have a many-body quantum system with a Hamiltonian $H$, also we know its ground states are degenerated given by $\psi_1, \psi_2,...\psi_N$.
Can the $N$ different degenerated ground states be transformed to each other without phase transition? Or in general these degenerated ground states may belong to different phases?