Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Abstract

Antiferromagnetic heavy fermion metals close to their quantum critical points display a richness in their physical properties unanticipated by the traditional approach to quantum criticality, which describes the critical properties solely in terms of fluctuations of the order parameter. This has led to the question as to how the Kondo effect gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent Bose-Fermi Kondo model within the Extended Dynamical Mean Field Theory. The quantum phase transition of the Kondo lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the present article we address some aspects of the failure of the standard order-parameter functional for the the Kondo-destroying quantum critical point of the Bose-Fermi Kondo model.

Scaling analysis in the numerical renormalization group study of the sub-Ohmic spin-boson model

“…Neither hyperscaling relations nor ω/T scaling should hold. However, variouls studies using BNRG 28 , QMC simulation [29][30][31] , ǫexpansion 26,32 and the large-N limit analysis 25,27,33 all point to the failure of the quantum-to-classical mapping in these systems: they obtained interacting fixed point and nonclassical exponents. Especially, for the anisotropic BFKM with a sub-Ohmic boson bath, the exponents are found to be the same as β N RG and δ N RG of the spin-boson model.…”

“…36 Much work has been done for this model, supporting the failure of the quantum-toclassical mapping in the sub-Ohmic regime. 27,30,36 Due to the very subtle nature of this problem, however, exact numerical studies are still desirable as a further confirmation. Both the isotropic and the anisotropic BFKM are at the core of studying the Kondo lattice with Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions using the extended dynamical mean-field theory.…”

Criticality of the mean-field spin-boson model: boson state truncation and its scaling analysis

“…They attributed the emergence of the interacting fixed point to the interference of the Berry phase [20]. In their recent work, S. Kirchner et al argued again that the presence of Berry phase changed the critical properties and claimed that the mapping theory failed for the sub-Ohmic BFKM [21]. A scaling analysis for the Ising-BFKM was performed in Ref.…”