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In normal fermi liquid theory, I saw that the mass is renormalized as

$$ \frac{m*}{m}=1+\frac{F_0}{3} $$

Recently I saw a couple talks on heavy fermion materials. One described, the fermi liquid behaviour in a very intuitive way:

In a material with a kondo impurity, the electrons can hybridize with the impurity and turn into a kondo insulator, but if you have a lattice of kondo impurities, translational symmetry is restored, the electrons can hop between them and the material becomes a fermi liquid.

In this picture, it appears that the electron wave functions are rather localized and conduct by dynamically jumping.

In another I saw the heavy fermion mass is re-normalized something like(I don't remember the exact form):

$$ \frac{m*}{m}=1+\frac{d}{d \omega} \Sigma(\omega) $$

The important point is it depended on the frequency dependence of the self energy. This seem really weird, particularly from the picture of the landau's effective energy picture, which doesn't include a frequency part. Furthermore it appears that the mass renormalization isn't a static property that describes a fermion wave function but is inherently tide to a dynamical response.

So my questions:

  1. What is the right equation for the renormalization of mass in heavy fermion materials?
  2. Why does it depend on frequency? Does this have something to do with dissipation?
  3. Can I imagine the electron wave function to be relatively localized in any sum of slater determines as the intuitive picture suggest and does this relate to the frequency dependence?
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  • $\begingroup$ The answer to question 2 is trivial: The effective mass does not depend on frequency (at least in standard FL theory), because in the correct formula the derivative is evaluated at the Fermi level $\omega=0$ (or $\omega=-\mu$, depending on definition). The correct formula is also $\frac{m*}{m}=1-\frac{d\Re\Sigma(\omega)}{d\omega}_{\omega=0}$. $\endgroup$ – Fitzgerald Creen Jun 16 '19 at 20:40

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