Nonergodic delocalized paramagnetic states in quantum neural networks

Typically, it is assumed that a high-energy eigenstate of a generic interacting quantum many-body Hamiltonian is thermal and obeys the eigenstate thermalization hypothesis. In this work, we show that the paramagnetic phase of a quantum Hopfield neural network model is delocalized but nonergodic. The combination of permutational symmetry and frustration in this model organize its high-energy eigenstates into clusters, which can each be considered a large quantum spin and has no correlation with others. This model provides another ergodicity-breaking mechanism in quantum many-body systems.