  Motivated by recent experiments on magnetically frustrated heavy fermion
metals, we theoretically study the phase diagram of the Kondo lattice model
with a nonmagnetic valence bond solid ground state on a ladder. A similar
physical setting may be naturally occurring in YbAl$_3$C$_3$, CeAgBi$_2$, and
TmB$_4$ compounds. In the insulating limit, the application of a magnetic field
drives a quantum phase transition to an easy-plane antiferromagnet, which is
described by a Bose-Einstein condensation of magnons. Using a combination of
field theoretical techniques and density matrix renormalization group
calculations we demonstrate that in one dimension this transition is stable in
the presence of a metallic Fermi sea and its universality class in the local
magnetic response is unaffected by the itinerant gapless fermions. Moreover, we
find that fluctuations about the valence bond solid ground state can mediate an
attractive interaction that drives unconventional superconducting correlations.
We discuss the extensions of our findings to higher dimensions and argue that,
depending on the filling of conduction electrons, the magnon Bose-Einstein
condensation transition can remain stable in a metal also in dimensions two and
three.
