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Quantum criticality and non-Fermi-liquid behavior in a two-level two-lead quantum dot

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.