Quantum Field Theoretical Study of Correlated Quantum Ising Model with Next-Nearest-Neighbour Interaction

We present the results of quantum Ising and longer range quantum Ising model for strongly correlated emergent Hamiltonian. We show explicitly that the ordered ferromagnetic (FM) phase to the disorder quantum paramagnet (dqpI) quantum phase transition occurs only in the strongly correlated regime for the quantum Ising model otherwise only dqpI phase appears for a non-interacting and attractive regime. We show that short-range FM coupling and longer range coupling are competing with each other and also the effect of strong correlation in this competition. We also show the most interesting feature that the transverse field opposes the FM coupling of quantum Ising model but it favours the longer range coupling. 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 the transition from dqpII phase to the FM phase. We also observe three different kinds of coexistence phases depending on the correlated regime. The fixed point analysis of the three sets of RG equations is carried out.