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

Abstract

The atomic dipoles in the Rabi lattice model exhibit quantum Ising dynamics in the limit of strong atom-photon interaction. It governs the paraelectric to ferroelectric 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 ${\ensuremath{\rho}}_{1L}^{x}={p}^{8}$ between the end-to-end dipole correlation ${\ensuremath{\rho}}_{1L}^{x}$ and the spontaneous polarization $p$ is proposed as an observable signature of these edge modes. The density-matrix renormalization-group 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 that protect the edge modes against the adverse perturbations are also identified.