Charge-Kondo circuits as quantum simulators*

Quantum nanoelectronic circuits, comprising charge-Kondo quantum dot components, offer a uniquely versatile and exquisitely controllable route to analog quantum simulation of complex models. In this work, we study the simplest one- and two-site systems, comparing experiment and theory to validate the models realized by such circuits. 

Already for a single charge-Kondo dot coupled to two or three leads, a frustration of screening produces distinctive quantum critical conductance signatures, with unprecedented agreement observed between experiment and theory for the two- and three-channel Kondo models. A new self-consistent relation between conductance and entropy is used to demonstrate the fractional entropy of these systems, establishing the charge-Kondo circuit as an accurate experimental quantum simulator of the model in a highly nontrivial regime, in which fractional Majorana or Fibonacci anyons are realized.

When two charge-Kondo sites are coupled together, we demonstrate that more complex many-body interactions are generated than arise with ultrasmall (spin) quantum dots, and that this opens up a richer range of possibilities for quantum simulation with such circuits. The experimental device is shown to realize a novel variant of the famous two-impurity Kondo model, in which local and collective Kondo screening processes compete. Universal properties of a new quantum critical point predicted from state-of-the-art numerical renormalization group calculations are confirmed experimentally.

These results lay the foundation for building more complex circuits, and scaling up from coupled dots to networks or lattices, where the experiment may yield the solution to otherwise computationally intractable models.