A grand aspiration of cavity quantum materials research is to uncover fundamentally new routes for controlling properties of matter by judiciously tailoring the quantum electromagnetic environment. Experiments with dark cavities revealed modified transport properties in the integer and fractional quantum Hall states of a 2D electron gas, as well as cavity-assisted thermal control of the metal-to-insulator transition in charge-density-wave systems.
Analogue quantum simulations are a useful tool for investigating these systems, particularly in regimes in which the applicability of numerical techniques is limited. For different simulator platforms, figures of merit include the electron bandwidth and interaction strength, temperature and the number of simulated lattice sites. Their use is further underscored by the ability to realize distinct lattice geometries, on-site degrees of freedom and by the physical observables that are accessible to experimental measurement.