Quantum phase transitions are usually observed in ground states of correlated systems.
Remarkably, eigenstate phase transitions can also occur at finite energy density in
disordered, isolated quantum systems. Such transitions fall outside the framework of
statistical mechanics as they involve the breakdown of ergodicity. Here, we consider what
general constraints can be imposed on the nature of eigenstate transitions due to the
presence of disorder. We derive Harris-type bounds on the finite-size scaling exponents of …