Quasiparticle density of states : how to give it a meaning as the quasi particle are interacting?

2017-10-20 11:18:41

There is something I don't understand about quasiparticles density of states.

I work with the book "Introduction to many body physics" from Coleman.

When he introduces the quasiparticle he does the following.

We consider a Fermi sea of a non interacting system.

Now we "enable" the interactions adiabatically. Thus we have an adiabatic correspondance between the non-interacting system and the interacting one. We can thus refer to the interacting system eigenstates by $ | \{n_{p \sigma} \rangle \} $ where $n_{p \sigma}$ is the occupation of electrons in the non interacting system (1-1 correspondance between the eigen states).

Now, he defines a quasiparticle by saying it is the fact to add a single electron above fermi sea and then enabling the interactions. We will end up with a state of the interacting system that has a single excitation. He calls this excitation a quasiparticle.

The energy of a single quasiparticle is then defined by :

$$ E^0_{p \sigma}=E(p,\sigma)-E