The observation of the quantum critical point in a series double quantum dot system depends on the distinct separation of two scales, $T_K⪢T^{\ast }$, where $T_K$ is the Kondo temperature and $T^{\ast }$ is the scale at which the system renormalizes away from the quantum critical point to a stable Fermi-liquid fixed point. Using the two-impurity Kondo model, we provide a derivation of $T^{\ast }$ based on the renormalization group (RG) to lowest order. This result is confirmed by a numerical RG (NRG) analysis which supplements the analytic derivation with additional quantitative precision. The form of the low-energy Fermi-liquid fixed point is derived and subsequently confirmed by the NRG. From this analysis, we conclude that the aforementioned separation of scales is satisfied, allowing the possibility that the quantum critical point may be measured in a future experiment on such double quantum dot systems.

• Received 25 August 2010

DOI:https://doi.org/10.1103/PhysRevB.82.205327