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We demonstrate for the first time that a functional-renormalization-groupaided density-functional theory (FRG-DFT) describes well the characteristicfeatures of the excited states as well as the ground state of an interactingmany-body system with infinite number of particles in a unified manner. TheFRG-DFT is applied to a $(1+1)$-dimensional spinless nuclear matter. For theexcited states, the density--density spectral function is calculated at thesaturation point obtained in the framework of FRG-DFT, and it is found that ourresult reproduces a notable feature of the density--density spectral functionof the non-linear Tomonaga-Luttinger liquid: The spectral function has asingularity at the edge of its support of the lower-energy side. These findingssuggest that the FRG-DFT is a promising first-principle scheme to analyze theexcited states as well as the ground states of quantum many-body systemsstarting from the inter-particle interaction.

progress of theoretical and experimental physics

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