Local fluctuations in quantum critical metals

Abstract

We show that spatially local, yet low-energy, fluctuations can play an essential role in the physics of strongly correlated electron systems tuned to a quantum critical point. A detailed microscopic analysis of the Kondo lattice model is carried out within an extended dynamical mean-field approach. The correlation functions for the lattice model are calculated through a self-consistent Bose-Fermi Kondo problem, in which a local moment is coupled both to a fermionic bath and to a bosonic bath (a fluctuating magnetic field). A renormalization-group treatment of this impurity problem--perturbative in $\epsilon=1-\gamma$, where $\gamma$ is an exponent characterizing the spectrum of the bosonic bath--shows that competition between the two couplings can drive the local-moment fluctuations critical. As a result, two distinct types of quantum critical point emerge in the Kondo lattice, one being of the usual spin-density-wave type, the other ``locally critical.'' Near the locally critical point, the dynamical spin susceptibility exhibits $\omega/T$ scaling with a fractional exponent. While the spin-density-wave critical point is Gaussian, the locally critical point is an interacting fixed point at which long-wavelength and spatially local critical modes coexist. A Ginzburg-Landau description for the locally critical point is discussed. It is argued that these results are robust, that local criticality provides a natural description of the quantum critical behavior seen in a number of heavy-fermion metals, and that this picture may also be relevant to other strongly correlated metals.Comment: 20 pages, 12 figures; typos in figure 3 and in the main text corrected, version as publishe

Entanglement entropy near Kondo-destruction quantum critical points

“…Here, we study variants of these models that exhibit critical destruction of the Kondo effect, where Kondo screening is suppressed at a second-order quantum phase arising from the presence of a pseudogap in the conduction-band density of states around the Fermi energy [10][11][12][13][14][15][16][17][18] and/or an additional coupling of the impurity to a bosonic environment [19][20][21][22][23][24][25] . Kondo destruction QCPs in the Bose-Fermi Kondo model have been proposed to describe anomalous quantum criticality in heavy fermion metals 26,27 and non-equilibrium criticality in a quantum dot with ferromagnetic leads 28 . Pseudogap Kondo and Anderson models have been used to study nonmagnetic impurities in d-wave superconductors 29 and in graphene 30 .…”

Quantum critical Kondo destruction in the Bose-Fermi Kondo model with a local transverse field

“…The spin-densitywave QCPs 5 represent the quantum-mechanical extension of the classical Landau-Ginzburg-Wilson framework, describing criticality solely in terms of fluctuations of a magnetic order parameter. By contrast, the locally critical picture [6][7][8] is "beyond-Landau" in that it invokes the destruction of the heavy quasiparticles at the transition. Such a Kondo destruction introduces new critical degrees of freedom beyond orderparameter fluctuations.…”

“…6,7,[15][16][17][18] More recently, the notion of Kondo destruction has been incorporated into a global zero-temperature phase diagram for heavy fermions. 19 The phase diagram, proposed for the Kondo lattice model, is shown in Fig.…”

“…Such a Kondo destruction introduces new critical degrees of freedom beyond orderparameter fluctuations. A microscopic theory of local quantum criticality 6,7 has been formulated in terms of extended dynamical mean-field theory (EDMFT), 9,10 in which the Kondo lattice model is mapped to an effective quantum impurity problem: the Bose-Fermi Kondo model (BFKM) with selfconsistently determined densities of states for the fermionic conduction band and for the bosonic bath.…”

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

“…Within EDMFT, the local quantum critical point of the lattice problem is related to the quantum critical point (QCP) of a dissipative BFK model [18,19,20]. If the self-consistency condition leads to a spectral density for the bosonic bath that behaves as…”