  Atoms trapped in microcavities and interacting through the exchange of
virtual photons can model an anisotropic Heisenberg spin-1/2 lattice.
  We do the quantum field theoretical study of such a system using the Abelian
bosonization method followed by the renormalization group analysis. We present
interesting physics due to the presence of exchange anisotropy. An infinite
order Kosterliz-Thouless-Berezinskii transition is replaced by second order XY
transition even an infinitesimal a small anisotropy in exchange coupling is
introduced. We predict a quantum phase transition between Mott insulating and
photonic superfluid phase due to detuning between the cavity and laser
frequency, a large detuning favours the photonic superfluid phase. We also do
the analysis of Jaynes and Cumming Hamiltonian to support results of quantum
field theoretical study.
