Hohenberg-Kohn-theorem-inspired functional renormalization-group analysis of ground and excited states of a one-dimensional nuclear matter*

We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) and the density-density spectral function of an infinite nuclear matter (NM) in (1+1) dimensions composed of spinless nucleons. The resultant EOS of the NM coincides with that obtained by the Monte-Carlo method within a few percent for the available range of density. We also reproduce a notable feature of the density density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has singularities at the edge of its support at the lower-energy side. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantum many-body theory.