An ab initio approach is presented for studying the collective excitations in excitonic insulators, charge/spin density waves, and superconductors. We derive the Bethe-Salpeter equation for the particle-hole excitations in the quasiparticle representation, from which the collective excited states are solved and the corresponding order parameter fluctuations are computed. This method is demonstrated numerically for the excitonic insulating phases of the biased ${\mathrm{WSe}}_2\text{−}{\mathrm{MoSe}}_2$ bilayer. It reveals the gapless phase mode, the subgap Bardasis-Schrieffer modes, and the above-gap scattering states. Our work paves the way for quantitative predictions of excited state phenomena from first-principles calculations in electronic systems with spontaneous symmetry breaking.

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• Excitons
• Optical conductivity
• Quasiparticles & collective excitations
• Bose-Einstein condensates
• Transition metal dichalcogenides
• Approximation methods for many-body systems
• Bethe-Salpeter equation
• First-principles calculations