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We study a strongly interacting "quantum dot 1" and a weakly interacting "dot2" connected in parallel to metallic leads. Gate voltages can drive the systembetween Kondo-quenched and non-Kondo free-moment phases separated byKosterlitz-Thouless quantum phase transitions. Away from the immediate vicinityof the quantum phase transitions, the physical properties retain signatures offirst-order transitions found previously to arise when dot 2 is strictlynoninteracting. As interactions in dot 2 become stronger relative to thedot-lead coupling, the free moment in the non-Kondo phase evolves smoothly froman isolated spin-one-half in dot 1 to a many-body doublet arising from theincomplete Kondo compensation by the leads of a combined dot spin-one. Theselimits, which feature very different spin correlations between dot and leadelectrons, can be distinguished by weak-bias conductance measurements performedat finite temperatures.

Signatures of quantum phase transitions in parallel quantum dots: Crossover from local-moment to underscreened spin-1 Kondo physics