  Analytical and continuous-time quantum Monte Carlo methods are used to
investigate the possibility of occupation switching and quantum criticality in
a model of two quantum impurities coupled to two leads. A general discussion of
potential occupancy-switching related quantum critical points is given, and a
detailed analysis is made of a specific model which has been recently
discussed. For spinless electrons, no phase transition is found. For electrons
with spin, a critical value of the interaction strength separates a weak
coupling regime in which all properties vary smoothly with parameters from a
strong coupling phase in which occupation numbers vary discontinuously as level
energies are changed. The discontinuity point is characterized by
non-Fermi-liquid behavior. Results for self-energies and correlation functions
are given. Phase diagrams are presented.
