  Quantum criticality beyond the Landau paradigm represents a fundamental
problem in condensed matter and statistical physics. Heavy fermion systems with
multipolar degrees of freedom can play an important role in the search for its
universal description. We consider a Kondo lattice model with both spin and
quadrupole degrees of freedom, which we show to exhibit an antiferroquadrupolar
phase. Using a field theoretical representation of the model, we find that
Kondo couplings are exactly marginal in the renormalization group sense in this
phase. This contrasts with the relevant nature of the Kondo couplings in the
paramagnetic phase and, as such, it implies that a Kondo destruction and a
concomitant small to large Fermi surface jump must occur as the system is tuned
from the antiferroquadrupolar ordered to the paramagnetic phase. Implications
of our results for multipolar heavy fermion physics in particular and metallic
quantum criticality in general are discussed.
