Interaction-mitigated Landau damping

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 (moir\'e) graphene-like systems.