Ab initio description of excited states of 1D uniform matter with the Hohenberg–Kohn-theorem-inspired functional-renormalization-group method

We demonstrate for the first time that a functional-renormalization-group aided density-functional theory (FRG-DFT) describes well the characteristic features of the excited states as well as the ground state of an interacting many-body system with an infinite number of particles in a unified manner. The FRG-DFT is applied to (1+1) D spinless nuclear matter. For the excited states, the density–density spectral function is calculated at the saturation point obtained in the framework of FRG-DFT, and it is found that our result reproduces a notable feature of the density–density spectral function of the nonlinear Tomonaga–Luttinger liquid: The spectral function has a singularity at the edge of its support on the lower-energy side. These findings suggest that the FRG-DFT is a promising first-principles scheme to analyze the excited states as well as the ground states of quantum many-body systems starting from the inter-particle interaction