  We present a spin model, namely, the Kitaev model augmented by a loop term
and perturbed by an Ising Hamiltonian and show that it exhibits both
confinement-deconfinement transitions from spin liquid to
antiferromagnetic/spin-chain/ferromagnetic phases and topological quantum phase
transitions between gapped and gapless spin liquid phases. We develop a
Fermionic mean-field theory to chart out the phase diagram of the model and
estimate the stability of its spin liquid phases which might be relevant for
attempts to realize the model in optical lattices. We also conjecture that some
of the confinement-deconfinement transitions in the model, predicted to be
first order within the mean-field theory, may become second order via a defect
condensation mechanism.
