  The physics of quantum Ising model (qIm) plays an important role in quantum
many body system. We study and present the results of qIm and longer range
quantum Ising model (lqIm) in presence of strong correlation. We do the quantum
field theoretical renormalization group (RG) calculation to study the behaviour
of RG flow lines for different couplings for different region of parameter
space. We show how the strong correlation effect enrich the quantum physics of
these two systems. We show explicitly that the ordered ferromagnetic (FM) phase
to the disorder quantum paramagnet (dqpI) quantum phase transition occurs for
only in the strongly correlated regime for qIm and the dqpI phase appears for
non-interacting and attractive regime. We show explicitly for lqIm that FM to
dqpI transition occurs at the extremely correlated region and also the dqpI
phase appears in correlated regime. We show that short range FM coupling and
longer range coupling are competiting with each other and also the effect of
strong correlation in this competition. We also show the most interesting
feature that the transverse field oppose the FM coupling of qIm but it is
favour the longer range coupling of lqIm. We find the evidence of another
disorder quantum paramagnetic (dqpII) phase due to the relevance of longer
range coupling. We also present the existence of another quantum phase
transition from dqpII phase to FM phase. We show explicitly that there is no
phase transition from dqpI phase to dqpII phase rather they coexists. This work
provides a new perspective not only for the statistical physics of quantum
Ising model but also for the quantum many body systems.
