I am considering the Heisenberg XXZ model at the moment. In the literature it says that (in the $J\Delta\rightarrow\infty$ limit, i.e. the ferromagnetic Ising regime) one can either view low-energy excitations as magnons (single overturned spins), or as domains of consecutive flipped spins, named spinons. The latter is supposed to have spin $S=1$. My question is two-fold:

-How do we easily note the statistics of the introduced particle and what spin it has?

-When do we choose what quasi-particle?


The spin of a quasiparticle can be determined from a number of ways:

  • If the quasi-particle is a "compound" object, you just add the individual spins according to the appropriate rules for adding angular momenta. An example would be the polaron, which is an electron dressed with a bunch of phonons. The electron has spin $1/2$, the phonons have spin $0$, so the total object has spin $1/2$.
  • If the quasi-particle is more like a collective excitation (magnon, spinon), just compare the total spin of a system with and without the thing. The difference must then be the spin of your particle. Consider a ferromagnet of spin $1/2$ magnetic moments in its ground-state with all spins pointing in the same direction. The total spin is then $N/2$ where $N$ is the number of moments. Flipping a single spin means the total spin is now $(N-1)/2 - 1/2 = N/2 - 1$, so the newly created excitation has spin 1.

For your question "when do we choose what quasi-particle", that is a bit more subtle and boils down to what you want to do. If representations are equivalent, so choose whatever is more convenient for calculations or visualizations.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.