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The goal of this paper is to relate the capacitance matrix formalism to thetight-binding approximation. By doing so, we open the way to the use ofmathematical techniques and tools from condensed matter theory in themathematical and numerical analysis of metamaterials, in particular for theunderstanding of their topological properties. We firstly study how thecapacitance matrix formalism, both when the material parameters are static andmodulated, can be posed in a Hamiltonian form. Then, we use this result tocompare this formalism to the tight-binding approximation. We prove that thecorrespondence between the capacitance formulation and the tight-bindingapproximation holds only in the case of dilute resonators. On the other hand,the tight-binding model is often coupled with a nearest-neighbourapproximation, whereby long-range interactions are neglected. Even in thedilute case, we show that long-range interactions between subwavelengthresonators are relatively strong and nearest-neighbour approximations are notgenerally appropriate.

On the validity of the tight-binding method for describing systems of subwavelength resonators