Fast Ground-State Reordering from Off-Diagonal Fluctuations of Interaction

It is shown that off-diagonal fluctuations of interaction lead to the breakdown of perturbation theory in the immediate vicinity of the ground-state of a fermionic system at a rate inversely proportional to the number of considered particles. This rate is parametrically much faster than previously expected. It is shown that this follows from the coherent addition of many small second order contributions to the energy of low-lying levels.