Quantum phase transition and emergent symmetry in a quadruple quantum dot system.

We propose a system of four quantum dots designed to study the competition between three types of interactions: Heisenberg, Kondo, and Ising. We find a rich phase diagram containing two sharp features: a quantum phase transition (QPT) between charge-ordered and charge-liquid phases and a dramatic resonance in the charge liquid visible in the conductance. The QPT is of the Kosterlitz-Thouless type with a discontinuous jump in the conductance at the transition. We connect the resonance phenomenon with the degeneracy of three levels in the isolated quadruple dot and argue that this leads to a Kondo-like emergent symmetry from left-right Z2 to U(1).