Bosonic collective modes are ubiquitous in metals, but over a wide range of energy and momenta suffer from Landau damping, decaying into the continuum of particle-hole excitations. Here we point out that interactions can suppress this decay, protecting a finite fraction of the total spectral weight associated with the collective mode, e.g., a plasmon. The underlying mechanism is level repulsion between a discrete mode and the continuum. We demonstrate the effect using a number of simplified models of strongly correlated Fermi-liquid metals, including a solvable random flavor model in the large-$N$ limit. We discuss in detail the possibility of observing such an avoided decay for plasmons in (moiré) graphenelike systems.

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• Lifetimes & widths
• Plasmonics
• Plasmons
• Quasiparticles & collective excitations
• Graphene
• Random phase approximation