Analysis of low energy response and possible emergent SU(4) Kondo state in a double quantum dot

We examine the low energy behavior of a double quantum dot in a regime where spin and pseudospin excitations are degenerate. The individual quantum dots are described by Anderson impurity models with an on-site interaction $U$ which are capacitively coupled by an interdot interaction $U_{12}<U$. The low energy response functions are expressed in terms of renormalized parameters, which can be deduced from an analysis of the fixed point in a numerical renormalization group calculation. At the point where the spin and pseudospin degrees of freedom become degenerate, the free quasiparticle excitations have a phase shift of $\pi/4$ and a 4-fold degeneracy. We find, however, when the quasiparticle interactions are included, that the low energy effective model has SU(4) symmetry only in the special case $U_{12}=U$ unless both $U$ and $U_{12}$ are greater than $D$, the half-bandwidth of the conduction electron bath. We show that the gate voltage dependence of the temperature dependent differential conductance observed in recent experiments can be described by a quasiparticle density of states with temperature dependent renormalized parameters.