Low-energy transition in spectral statistics of two-dimensional interacting fermions

Pil Hun Song, Dima L. Shepelyansky
2000 Physical Review B (Condensed Matter)  
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.
doi:10.1103/physrevb.61.15546 fatcat:mif3beb4nffxrau57rnspz4xdq