Given a hamiltonian, I compute the Hartree-Fock self-energy. Let's say I now compute the second order self-energy with diagrams. Some of them are just like the Hartree or Fock diagrams of first order, but with the Green functions in the middle dressed. Do I need to include these diagrams in the second order calculation, or would that imply a double-counting? For example, the second order tadpole diagram is clearly a Hartree diagram, but I'm not sure if computing it and adding it to my perturbative self-energy is double-counting, given that my non-perturbed hamiltonian already includes the Hartree-Fock potential.

Edit: By doing the computations in a particular and simple case, I've found that the answer is that those diagrams must be left out (they are implicitely included in the mean-field-like HF self-energy), but I don't have a satisfactory general argument. Also, if I compute the energy with Goldstone diagrams, would I need to include the second order diagrams such as the double exchange diagram or the one coming from the tadpole/hartree one, if I already have the HF mean-field contribution to the energy? I'm not sure, although I suspect the answer is again "no".

  • $\begingroup$ Only one particle irreducible diagrams contribute to self energy (perturbative). When you dress up propagators appearing in self energy you resum more diagrams. $\endgroup$ – Sunyam Oct 2 '18 at 19:13

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