Editing QuasiParticles (section)

=== Heisenberg Model for Magnons ===
Magnons, as spin wave quasiparticles, are described by the Heisenberg exchange interaction. The Hamiltonian for a system of interacting spins is:

<math>H = -J \sum_{\langle i,j \rangle} \mathbf{S}_i \cdot \mathbf{S}_j</math>

where:
* <math>H</math> is the Hamiltonian representing the total energy of the system,
* <math>J</math> is the exchange constant, which determines the strength of the interaction,
* <math>\mathbf{S}_i</math> and <math>\mathbf{S}_j</math> are the spin vectors at sites <math>i</math> and <math>j</math>,
* The summation is over all nearest-neighbor pairs <math>\langle i,j \rangle</math>.

This equation helps explain the collective spin excitations in ferromagnetic and antiferromagnetic materials.