Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench

The atoms trapped in microcavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We study the dynamics of the geometric phase of this system under the linear quenching process of laser field detuning which shows the XX criticality of the geometric phase in presence of single Rabi frequency oscillation. We also study the quantum criticality for different quenching rate in the presence of single or two Rabi frequencies oscillation in the system.