Absence of quantum phase transition in two-state quantum dot*

We use continuous-time quantum Monte Carlo methods to study a model of a spinless-fermion two state quantum dot which was argued in Ref. [1] to exhibit a quantum phase transition. We find instead a smooth behavior as parameters are varied. The generalization of the model to the spinful case is also presented. [1] D. I. Golosov and Y. Gefen, {\em Phys. Rev. B} {\bf 74}, 205316 (2006).