We theoretically investigate criticality and multifractal states in a one-dimensional Aubry-André-Harper model coupled to electromagnetic cavities. We focus on two specific cases where the photon frequencies are ${\omega }_0=1$ and 2, respectively. Phase transitions are analyzed using both the average and minimum inverse participation ratio to identify metallic, fractal, and insulating states. We provide numerical evidence to show that the presence of the optical cavity induces a critical, intermediate phase in between the extended and localized phases, hence drastically modifying the traditional transport phase diagram of the Aubry-André-Harper model, in which critical states can only exist at the well-defined metal-insulator critical point. We also investigate the probability distribution of the inverse participation ratio and conduct a multifractal analysis to characterize the nature of the critical phase, in which we show that extended, localized, and fractal eigenstates coexist. Altogether, our findings reveal the pivotal role that the coupling to electromagnetic cavities plays in tailoring critical transport phenomena at the microscopic level of the eigenstates.

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• Anderson localization
• Light-matter interaction
• Polarons
• 1-dimensional systems
• Quasicrystals
• Numerical techniques