Saturday, January 2, 2010

|→ Quasiparticles

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 — quasi2 ...). [For composite Fermions ↔ gravity, have a look at Bak, Rey, arXiv:0912.0939.]


  1. The Kohn-Sham system is of auxiliary nature only rather than being a quasiparticle model.

  2. True that the Kohn-Sham "bandstructure" doesn't carry too much single-particle spectral information. Still interesting how the theorems of DFT enable you to construct effective single-particle like Hamiltonians.

  3. higher dimensional models can be generated by twisting transformation which preserves integrability hep-th/9612046

  4. Increasing the dimension by twisting is interesting. Yet the result is only quasi-multidimensional (interchain coupling). Is there a way to create "densely coupled" integrable multidimensional models?

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  6. Hi there,
    I like very much the idea of your compcondmat blog. I just find it somewhat beyond my level. How about a few more basic descriptions to give us experimentalists a better understanding? It would be much appreciated.

  7. Hi Jonah,
    You're absolutely right.
    Which field would you be interested in?

  8. Hey QuasiNewton,
    Most of the things you've discussed so far are relevant and interesting to me (quantum simulation, quasiparticles). I don't know where you're going to take the blog, but I would suggest including the 'basic' descriptions that would help out folks like myself.

    How about delving into more detail in some of those quasiparticle issues? For example, how do these emerge theoretically in the different cases you mentioned? I've been wondering, for example, what's the difference between the effective bosonic modes of a Tomonaga-Luttinger-type 1D model and the quasiparticle of a Fermi system. Surely they both describe the effective low-energy excitations, and yet the Luttinger-type model has no lifetime requirement (that I know of).

    Anything you throw out there, I'm likely to find interesting, so I guess I'll just keep asking questions.

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  10. With the adiabatic turn-on of the interaction in Fermi liquid theory, there is a (weak) residual interaction between the quasiparticles leading to finite lifetime, which behaves like (E-E_F)**-2 for excitations in the vicinity of E_F because of the Pauli blockade.
    The bosonization in Luttinger liquid theory leads to a model of non-interacting (i.e. with infinite lifetime) bosonic excitations with linear dispersion. That is, there is indeed no lifetime requirement for the theory. In experimental realizations of Luttinger liquids there will be finite lifetimes due to e.g. finite band curvature, which makes the corresponding density waves "collide".
    The following paper by Biermann et al.: PRL 87, 276405 (2001) (preprint: arXiv:cond-mat/0107633) provides a dynamical mean field theory study of the transition from a Luttinger liquid 1D system to a quasi 1D Fermi liquid system.