  It is believed that the two-dimensional (2D) Anderson model exhibits
localization for any nonzero disorder in the thermodynamic limit and it is also
well known that the finite-size effects are considerable in the weak disorder
limit. Here we numerically study the quantum-chaos to localization transition
in the finite 2D Anderson model using standard indicators used in the modern
literature such as the level spacing ratio, spectral form factor, variances of
observable matrix elements, participation entropy and the eigenstate
entanglement entropy. We show that many features of these indicators may
indicate emergence of robust single-particle quantum chaos at weak disorder.
However, we argue that a careful numerical analysis is consistent with the
single-parameter scaling theory and predicts the breakdown of quantum chaos at
any nonzero disorder value in the thermodynamic limit. Among the hallmarks of
this breakdown are the universal behavior of the spectral form factor at weak
disorder, and the universal scaling of various indicators as a function of the
parameter $u = \left(W \ln V\right)^{-1}$ where $W$ is the disorder strength
and $V$ is the number of lattice sites.
