Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

We study theoretically a ring of three quantum dots mutually coupled by antiferromagnetic exchange interactions and tunnel-coupled to two metallic leads: the simplest model in which the consequences of local frustration arising from internal degrees of freedom may be studied within a two-channel environment. Two-channel Kondo (2CK) physics is found to predominate at low energies in the mirror-symmetric models considered, with a residual spin-1/2 overscreened by coupling to both leads. It is however shown that two distinct 2CK phases, with different ground-state parities, arise on tuning the interdot exchange couplings. In consequence a frustration-induced quantum phase transition occurs, the 2CK phases being separated by a quantum critical point for which an effective low-energy model is derived. Precisely at the transition, parity mixing of the quasidegenerate local trimer states acts to destabilize the 2CK fixed points; and the critical fixed point is shown to consist of a free pseudospin together with effective one-channel spin quenching, itself reflecting underlying channel anisotropy in the inherently two-channel system. Numerical renormalization group techniques and physical arguments are used to obtain a detailed understanding of the problem, including study of both thermodynamic and dynamical properties of the system.