Quantum phase transitions in systems of parallel quantum dots

Abstract

We study the low-temperature transport properties of systems of parallel quantum dots described by the $N$-impurity Anderson model. We calculate the quasiparticle scattering phase shifts, spectral functions, and correlations as a function of the gate voltage for $N$ up to 5. For any $N$, the conductance at the particle-hole symmetric point is unitary. For $N\ensuremath{\ge}2$, a transition from ferromagnetic to antiferromagnetic impurity spin correlations occurs at some gate voltage. For $N\ensuremath{\ge}3$, there is an additional transition due to an abrupt change in average impurity occupancy. For odd $N$, the conductance is discontinuous through both quantum phase transitions, while for even $N$ only the magnetic transition affects the conductance. Similar effects should be experimentally observable in systems of quantum dots with ferromagnetic conduction-band-mediated interdot exchange interactions.