  Although the oscillator strength sum rule forbids the phase transition in
ideal non-interacting two-level atoms systems, we present the possibility of
the quantum phase transition in the coupled two-level atoms in a cavity. The
system undergoes the superradiant phase transition in the thermodynamics limit
and this transition is account for the atom-atom attractive interaction,
exhibiting a violation of the sum rule. The bosonic coherent state technique
has been adopted to locate the quantum critical point accurately in the
finite-size system. We predict the existence of the superadiant phase
transition as the number of atoms increases, satisfying all the constraints
imposed by the sum rule.
