Quantum critical scaling beyond Ginzburg-Laudau-Wilson paradigm in heavy-fermion metals

Within the standard bosonic Ginzburg-Landau-Wilson (G-L-W) theory of phase transitions, the hyperscaling ansatz exists only below the upper critical dimension (d+z < 4) with d being spacial dimension and z being the dynamical exponent. Surprisingly, however, we show that the hyperscaling ansatz can survive above the upper critical dimension (d+z > 4) in an effective field theory of a large-N approach to the Kondo-Heisenberg lattice model, relevant for describing a wide range of heavy-fermion materials. A novel Bose-Fermi effective field theory is constructed beyond our large-N saddle-point solution. Via perturbative renormalization group approach, a nontrivial interacting Gaussian fixed point is discovered due to the presence of a boson-fermion (Yukawa) coupling in our field theory, giving rise to novel hyperscaling relations beyond the G-L-W paradigm. The outstanding open issues on the singular-in-temperature behaviors for the specific heat coefficient and the Gruneisen ratio in the strange metal regime observed in heavy-fermion metal Ge-substituted YbRh₂Si₂ are well accounted for within our theory. The implications of our results to heavy-fermion quantum criticality, in general, are discussed.