Ab-initio description of ground and excited states of a one-dimensional nuclear matter with the Hohenberg--Kohn-theorem-inspired functional-renormalization-group method

Takeru Yokota, Kenichi Yoshida, Teiji Kunihiro

Published 2018-09-30Version 1

We demonstrate for the first time that a density-functional-theory-aided functional-renormalization-group (DFT-RG) method describes well the characteristic features of the ground and excited states of an interacting many-body system in a unified manner. The DFT-RG method is applied to a $(1+1)$-dimensional spinless nuclear matter. For the ground state, the equation of state (EOS) is calculated, and it is shown that the resultant saturation energy, which is derived from the minimum point of the EOS with respect to the density, is found to be close to the result of the Monte Carlo simulation. For the excited states, the density--density spectral function is calculated, and it is found that our result reproduces a notable feature of the density--density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has a singularity at the edge of its support of the lower-energy side. These findings suggest that the DFT-RG method is a promising first-principle scheme to analyze the excited states as well as the ground states of quantum many-body systems starting from the inter-particle interaction.