  We study theoretically a triangular cluster of three magnetic impurities,
hybridizing locally with conduction electrons of a metallic host. Such a
cluster is the simplest to exhibit frustration - an important generic feature
of many complex molecular systems in which different interactions compete.
Here, low-energy doublet states of the trimer are favored by effective exchange
interactions produced by strong electronic repulsion in localized impurity
orbitals. Parity symmetry protects a level-crossing of such states on tuning
microscopic parameters, while an avoided crossing arises in the general
distorted case. On coupling to a metallic host, the behavior is shown to be
immensely rich, since collective quantum many-body effects now also compete. In
particular, impurity degrees of freedom are totally screened at low
temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground
states persist in a local moment phase. Local frustration drives the quantum
phase transition between the two, which may be first order or of
Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local
moment formation and Kondo screening are found, due to the orbital structure of
the impurity trimer. Our results are of relevance for triple quantum dot
devices. The problem is studied by a combination of analytical arguments and
the numerical renormalization group.
