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The non-Hermitian dynamics of open systems deal with how intricate coherenteffects of a closed system intertwine with the impact of coupling to anenvironment. The system-environment dynamics can then lead to so-calledexceptional points, which are the open-system marker of phase transitions,i.e., the closing of spectral gaps in the complex spectrum. Even in theubiquitous example of the damped harmonic oscillator, the dissipativeenvironment can lead to an exceptional point, separating between under-dampedand over-damped dynamics at a point of critical damping. Here, we examine thefate of this exceptional point in the presence of strong correlations, i.e.,for a nonlinear oscillator. By employing a functional renormalization groupapproach, we identify non-perturbative regimes of this model where thenonlinearity makes the system more robust against the influence of dissipationand can remove the exceptional point altogether. The melting of the exceptionalpoint occurs above a critical nonlinearity threshold. Interestingly, theexceptional point melts faster with increasing temperatures, showing asurprising flow to coherent dynamics when coupled to a warm environment.

Fate of exceptional points in the presence of nonlinearities