  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.
