Integrability-chaos transition for lattice fermions

A multi-body system of spinless fermions on a tight-binding two-dimensional lattice is considered. In the absence of interactions between the fermions, the system is integrable and its energy spectrum becomes non-degenerate thanks to the twisted periodic boundary conditions and hoppings that change both coordinates. The integrability is lifted by the nearest-neighbor interactions. The integrability-chaos transition is characterized by statistical properties of the energy spectra and by fluctuations of observable expectation values over eigenstates. When the interaction strength increases, the level spacing ratio demonstrates the change of the energy spectrum statistics from the Poisson to the Wigner-Dayson one. At the same time, the fluctuation variance is substantially suppressed, demonstrating the approach of the eigenstate thermalization regime. When the number of fermions is increased, the transition to quantum chaos takes place at lower interaction strengths.