Abstract
We present a novel technique to obtain exact equation of state (EoS) by the Functional Renormalization Group (FRG) method, using the expansion of the effective potential in a base of harmonic functions at finite chemical potential. Within this theoretical framework we determined the equation of state and the phase diagram of a simple model of massless fermions coupled to scalars through Yukawa-coupling at the zero-temperature limit. We compared our results to the 1-loop and the mean field approximation of the same model and other high-density nuclear matter equation of states. We found a $10-20\%$ difference between these approximations. As an application, we used our exact, FRG-based equation of states to test the effect of the quantum fluctuations in superdense nuclear matter of a compact astrophysical object for the first time. We calculated the mass-radius relation for a compact star using the Tolmann-Oppenheimer-Volkov equation and observed a $\sim 5\%$ effect in compact star observables due to quantum fluctuations.
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