Low energy transition in spectral statistics of 2D interactingfermions

We study the level spacing statistics $P(s)$ and eigenstate properties of spinless fermions with Coulomb interaction on a two dimensional lattice at constant filling factor and various disorder strength. In the limit of large lattice size, $P(s)$ undergoes a transition from the Poisson to the Wigner-Dyson distribution at a critical total energy independent of the number of fermions. This implies the emergence of quantum ergodicity induced by interaction and delocalization in the Hilbert space at zero temperature.