Quantum phase transitions in the systems of parallel quantum dots

TL;DR

This paper investigates quantum phase transitions in parallel quantum dot systems, analyzing how conductance and impurity correlations change with gate voltage for different numbers of dots, revealing multiple phase transitions.

Contribution

It provides a detailed analysis of quantum phase transitions in N-impurity Anderson models for parallel quantum dots, including conductance behavior and impurity correlations for N up to 5.

Findings

Conductance is unitary at particle-hole symmetry for all N.

Transition from ferromagnetic to antiferromagnetic correlations occurs for N >= 2.

Additional occupancy transition appears for N >= 3.

Abstract

We study the low-temperature transport properties of the 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 >= 2, a transition from ferromagnetic to antiferromagnetic impurity spin correlations occurs at some gate voltage. For N >= 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 the systems of quantum dots with ferromagnetic conduction-band-mediated inter-dot exchange interactions.