@article{ISI:000259690800043,
 abstract = {In the first part of this paper, we study the spin-S Kitaev model using
spin-wave theory. We discover a remarkable geometry of the
minimum-energy surface in the N-spin space. The classical ground states,
called Cartesian or CN-ground states, whose number grows exponentially
with the number of spins N, form a set of points in the N-spin space.
These points are connected by a network of flat valleys in the N-spin
space giving rise to a continuous family of classical ground states.
Further, the CN-ground states have a correspondence with dimer coverings
and with self-avoiding walks on a honeycomb lattice. The zero-point
energy of our spin-wave theory picks out a subset from a continuous
family of classically degenerate states as the quantum ground states;
the number of these states also grows exponentially with N. In the
second part, we present some exact results. For arbitrary spin S, we
show that localized Z(2) flux excitations are present by constructing
plaquette operators with eigenvalues +/- 1, which commute with the
Hamiltonian. This set of commuting plaquette operators leads to an exact
vanishing of the spin-spin correlation functions beyond nearest-neighbor
separation found earlier for the spin-1/2 model [G. Baskaran et al.,
Phys. Rev. Lett. 98, 247201 (2007)]. We introduce a generalized
Jordan-Wigner transformation for the case of general spin S and find a
complete set of commuting link operators similar to the spin-1/2 model,
thereby making the Z2 gauge structure more manifest. The Jordan-Wigner
construction also leads, in a natural fashion, to Majorana fermion
operators for half-odd-integer spin cases and hard-core boson operators
for integer spin cases strongly suggesting the presence of Majorana
fermion and boson excitations in the respective low-energy sectors.
Finally, we present a modified Kitaev Hamiltonian, which is exactly
solvable for all half-odd-integer spins; it is equivalent to an
exponentially large number of copies of spin-1/2 Kitaev Hamiltonians.},
 article-number = {115116},
 author = {Baskaran, G. and Sen, Diptiman and Shankar, R.},
 doi = {10.1103/PhysRevB.78.115116},
 issn = {1098-0121},
 journal = {PHYSICAL REVIEW B},
 month = {SEP},
 number = {11},
 times-cited = {42},
 title = {Spin-S Kitaev model: Classical ground states, order from disorder, and
exact correlation functions},
 unique-id = {ISI:000259690800043},
 volume = {78},
 year = {2008}
}