Quasiparticle models allow for a solution of certain many-particle problems and may also provide descriptive pictures. Examples in solid state physics are

- composite Fermions with a mean field approximation related to the attached flux

- effective-mass Hamiltonians, where the energetic dispersion is reproduced
- Kohn-Sham Hamiltonians, where an effective potential is adjusted such that a given density is obtained (self-consistently)

In the case of non-interacting quasiparticles, an efficient solution of the corresponding many-particle problem is possible. Furthermore, infinite interaction strength can be considered instead (or in addition to zero interaction strength in terms of interpolation; see

e.g. Seidl, Perdew, Kurth, PRL 84, 5070 (2000)). Although Kohn-Shamions are often over-interpreted as single electrons, I'd still say that they are neat quasiparticles since it's the best you can generally do with a single Slater determinant. Would be cool to have solvable, not low-dimensional models for Coulomb systems at finite interaction strength (not only for a KS Hamiltonian). Are there any?

Really awesome is/would be the emergence of a Fermi liquid from the Anti-de-Sitter/Conformal Field Theory correspondence — here, quasiparticle shape and position in the spectral function are approximately reproduced [

Cubrovic, Zaanen, Schalm, arXiv:0904.1993,

Science 325, 439 (2009)] (in the AdS/CFT correspondence itself, the product of string coupling and number of D-branes is kept fixed — quasi

^{2} ...). [For composite Fermions ↔ gravity, have a look at

Bak, Rey, arXiv:0912.0939.]