Up to now, I found myself still does not have a deep understanding of the honeycomb Kitaev model, and I got some naive questions about the ground states (GSs) of the this model:
(1) Consider a simple case that Jx=Jy=0, then the model reduces to H=Jz∑z linksSziSzj. It's obvious that H has highly degenerate GSs (degeneracy=2N, where N is the number of unit cells), and in each GS configuration, every two spins connected by a z link are aligned parallel (if Jz<0) or antiparallel (if Jz>0). Thus, each of these GSs corresponds to a spin configuration and is not a spin liquid (SL).
On the other hand, the Majorana exact solution tells us that the GS of H is a gapped SL.
So, does the exact solution just single out one of the highly degenerate GSs, which happens to be a SL (some certain manner of superposition of the above 2N spin configurations) ??
(2) Following question (1), if the exact solution does single out just one of the highly degenerate GSs of H, and how could this be?
According to Kitaev's discussion on P.19 in his paper, the GS is achieved by the vortex-free field configuration, which follows from a theorem proved by Lieb.
But shouldn't an exact solution gives all the 2N GSs ? Why only single out one which strongly contradicts the obviously correct GS degeneracy=2N ? Is there something wrong with applying the Lieb's theorem here ? I'm confused....
This post imported from StackExchange Physics at 2014-04-13 11:24 (UCT), posted by SE-user K-boy