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We develop a length-gauge formalism for treating one-dimensional periodiclattice systems in the presence of a photon cavity inducing light-matterinteraction. The purpose of the formalism is to remove mathematical ambiguitiesthat occur when defining the position operator in the context of thePower-Zienau-Woolley Hamiltonian. We then use a diagrammatic approach toanalyze perturbatively the interaction between an electronic quantum system anda photonic cavity mode of long wavelength. We illustrate the versatility of theformalism by studying the cavity-induced electric charge imbalance andpolarization in the Rice-Mele model with broken inversion symmetry.

Cavity-induced charge transfer in periodic systems: length-gauge formalism