Quantum Ising dynamics and Majorana-like edge modes in the Rabi lattice model

The atomic dipoles in the Rabi lattice model exhibit quantum Ising dynamics in the limit of strong atom-photon interaction. It governs the para- to ferro-electric phase transition in the ground state. On an open chain, it implies the existence of two Majorana-like, albeit topologically unprotected, edge modes in the ordered phase. The relation \rho^x_{1L}=p^8 between the end-to-end dipole correlation, \rho^x_{1L}, and the spontaneous polarization, p, is proposed as an observable signature of these edge modes. The DMRG calculations on the one-dimensional Rabi lattice support the strong coupling quantum Ising behavior, and correctly yield the proposed end-to-end dipole correlation. The conditions which protect the edge modes against the adverse perturbations are also identified.