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The rapid progress in quantum-optical experiments especially in the field ofcavity quantum electrodynamics and nanoplasmonics, allows to substantiallymodify and control chemical and physical properties of atoms, molecules andsolids by strongly coupling to the quantized field. Alongside such experimentaladvances has been the recent development of ab-initio approaches such asquantum electrodynamical density-functional theory (QEDFT) that is capable ofdescribing these strongly coupled systems from first-principles. To investigateresponse properties of relatively large systems coupled to a wide range ofphoton modes, ab-initio methods that scale well with system size becomerelevant. In light of this, we extend the linear-response Sternheimer approachwithin the framework of QEDFT to efficiently compute excited-state propertiesof strongly coupled light-matter systems. Using this method, we capturefeatures of strong light-matter coupling both in the dispersion and absorptionproperties of a molecular system strongly coupled to the modes of a cavity. Weexemplify the efficiency of the Sternheimer approach by coupling the mattersystem to the continuum of an electromagnetic field. We observe changes in thespectral features of the coupled system as Lorentzian line shapes turn intoFano resonances when the molecule interacts strongly with the continuum ofmodes. This work provides an alternative approach for computing efficientlyexcited-state properties of large molecular systems interacting with thequantized electromagnetic field.

Frequency-dependent Sternheimer linear-response formalism for strongly coupled light-matter systems