There exists a concept of "composite fermion" when refer to heavy fermion system, which means spin-flip and conducting electron can be combined together to form a new "composite fermion".

In details, interaction between local moment fermion $f$ and conducting fermion $c$ can be decomposed into following form under the mean-field level: $$J S_{\alpha \beta}(j) c_{j \beta}^{\dagger} c_{j \alpha} \longrightarrow \bar{V} f_{j \alpha}^{\dagger} c_{j \alpha}+V c_{j \alpha}^{\dagger} \mathrm{f}_{j \alpha}$$ the composite combination of spin and conduction electron are contracted into a single Fermi field: $$J \overbrace{S_{\alpha \beta}(j) c_{j \beta}^{\dagger}}=J f_{j \alpha}^{\dagger} \overbrace{f_{j \beta }^{\dagger}c_{j\beta}}\rightarrow V f_{j \alpha}^{\dagger}$$ where now $V$ is just the anomalous Green function: $$V=G_{cf}=-J\left\langle c_{j \beta}^{\dagger} f_{j \beta}\right\rangle$$ Then, we can approximately calculate this anomalous Green function $g(\tau)=-G_{cf}(\tau)$, and find that: $$g(\tau) \sim\left\{\begin{array}{ll}{ \ln \tau} & {\tau \ll 1} \\ {\frac{1}{\tau}} & {\tau \gg1}\end{array}\right.$$ and author concludes that The short-time logarithimic correlations between the spin-flip and electron ($τ \ll 1$ ) represent the weak-coupling interior of the composite fermion, whereas the long-time power law correlations reflect the development of the Fermi liquid correlations at long times.

My question

I am confused of the last augments, i.e. I can not understand the relation between this Green function and internal structure of composite particle. Furthermore, I even cannot understand the physical meaning of "internal structure" for composite fermion here. Could anyone help me, or gives some reference?

In Summary, this question can be concluded as: According to this answer, from the view of effective field theory, two boson/fermmion particles form a composite particle, the resulting state has internal structure. But I cannot know how to obtain and analyze internal structure? Reference about it is welcome!


  • Ch.17.8, Piers Coleman, Introduction to Many-Body Physics
  • Piers Coleman, Heavy fermions: Electrons at the Edge of Magnetism

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