One way to solve the Kitaev honeycomb model:
H=Jx∑x links,<ij>σxiσxj+Jy∑y links,<ij>σyiσyj+Jz∑z links,<ij>σziσzj.
is to represent the spin operators by Majorana fermions (arXiv:cond-mat/0506438) which makes the Hamiltonian in a (sort of) quadratic form in Majorana fermions. This Hamiltonian can in turn be written in a quadratic form in some Dirac fermions:
H=∑ijtija†iaj+H.C.
Now, it is my understanding that to find the ground state of the system, we must fill the lowest lying states by ai fermions.
Now, my question is: what is number of ai fermions, N in this system (which is a conserved quantity)? and how is it related to physics of the original spin model?
This post imported from StackExchange Physics at 2015-03-01 12:40 (UTC), posted by SE-user Hamed