The quantum vacuum energy for a hybrid comb of Dirac $delta$-$delta$ potentials is computed using the energy of the single $delta$-$delta$ potential over the real line that makes up the comb. The zeta function of a comb periodic potential is the continuous sum of zeta functions over the dual primitive cell of Bloch quasi-momenta. The result obtained for the quantum vacuum energy is non-perturbative in the sense that the energy function is not analytical for small couplings
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