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The numerical renormalization group is employed to study a double quantum(DQD) dot system consisting of two equivalent single-level dots, each coupledto its own lead and with a mutual capacitive coupling embodied in an interdotinteraction U', in addition to the intradot Coulomb interaction U. We focus onthe regime with two electrons on the DQD, and the evolution of the system onincreasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) isfound to persist robustly with increasing U'/U, before a rapid but continuouscrossover to (a) the SU(4) point U'=U where charge and spin degrees of freedomare entangled and the Kondo scale strongly enhanced; and then (b) acharge-Kondo state, in which a charge-pseudospin is quenched on coupling to theleads/conduction channels. A quantum phase transition of Kosterlitz-Thoulesstype then occurs from this Fermi liquid, strong coupling (SC) phase, to abroken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c.Our emphasis in this paper is on the structure, stability and flows between theunderlying RG fixed points, on the overall phase diagram in the (U,U')-planeand evolution of the characteristic low-energy Kondo scale inherent to the SCphase; and on static physical properties such as spin- andcharge-susceptibilities (staggered and uniform), including universality andscaling behaviour in the strongly correlated regime. Some exact results forassociated Wilson ratios are also obtained.Comment: 27 pages, 12 figure

Renormalization group study of capacitively coupled double quantum dots