Functional renormalization-group calculation of the equation of state of one-dimensional uniform matter inspired by the Hohenberg-Kohn theorem

We present to our knowledge the first successful functional renormalization group (FRG)-aided density-functional theory (DFT) calculation of the equation of state (EOS) of infinite nuclear matter (NM) in (1+1) dimensions composed of spinless nucleons. We give a formulation to describe infinite matters in which the flowing chemical potential is introduced to control the expectation value of the particle number during the flow. The resultant saturation energy of the NM coincides with that obtained by the Monte Carlo method within a few percent. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantum many-body theory.