Catherine Pépin: Kondo Breakdown as a Selective Mott Transition in the Anderson Lattice

Blog from talk presented in week 4.

In her talk Catherine Pépin presented results published recently in PRL (I. Paul, C.
Pépin, and M. Norman, PRL 98, 026402 (2007); C. Pépin, PRL 98, 206401, (2007)). The work was devoted to study of a Mott transition of the f electrons in the Anderson lattice. The model of the Anderson lattice offers a way to relate the Kondo breakdown (vanshing of the effective hyrbidization between the f and c bands) to a Mott transition of the f electrons. The suggested idea has analogies in description of the cuprates superconductors because both in the Anderson lattice and in the Hubbard model, there is a competition between the Coulomb and kinetic energies. When the Coulomb energy is stronger this can lead to a localization of the f-electrons. A spin liquid is needed to stabilize the localized phase, but both in the Anderson and the Hubbard model a spin liquid is believed to be apearing when one approaches the insulating state, at least in a slave boson treatment, used in the presented work. Around the QCP associated with the Mott transition, one observes flucutations of the hybridization. Using a fermionic representation for the localized spins the deconfined quantum critical point was studied within this model.
The main idea presented in the talk was that an unusual behavior in thermodynamics and transport might be due to critical fluctuations of a nonmagnetic order parameter associated with the vanishing energy scale T_{K}, where T_{K} is an efective Kondo temperature. To be more precise, the Kondo effect breaks down because the effective hybridization is renormalized to zero.
In the Anderson lattice this occurs exactly when the f electrons localize. This contrasts previous approaches based on critical contributions of paramagnons.
Expressing the spin varibles in terms of fermions one comes to a fermion model with quartic fermion interactions that is further studied using a mean field approximation for the slave bosons. As the next step, flucutations around this mean mean field were also taken into account, in order to describe the thermodynamics around the QCP.
Assuming that the mean field solution does not depend on coordinates it was shown that, above a very smal temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a resistivity that has a TlogT behavior. At the same time, it was found that the specific heat coefficient diverges logarithmically in temperature, which is in agreement with results of observation in a number of heavy fermion metals.

Dirk Morr asked:

Is the temperature dependence of the resistence linear?

Answer:
Above a certain temperature, the temperature dependence linear but it becomes quadratic below it.

Andrey Chubukov asked:
Why is the the crossover temperature so low?

Answer:
It depends on the interplay between the Fermi momenta of the two bands.

Ilya Vekhter asked:
Why was it that z=3 in the intermediate temperature regime?

Answer:
It is a q=0 transition. When the critical modes are damped by the
continum of the electrons, one gets z=3 (Landau damping).

Viktor Galitskii asked:
What kind of the spin liquid is needed?

Answer:
In the U(1) gauge theory one gets naturally a massless spin liquid.

Hartmut Monien asked to explain why te resistivity is quasi-linear in T?

Answer:
In this model, the f-electrons llocalize and form a reservoir. Hence,
although one has a q=0 transition (hybridization fluctuations ) one does
not need impurities to break translational invariance: the f electrons are
on the lattice, which leads to umklapps. Then, the one impurity life time
is the same as the transport lifetime-- quite a unique feature.