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.
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