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

Abstract

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 infinite number of particles in a unified manner. The FRG-DFT is applied to a $(1+1)$-dimensional 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 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 FRG-DFT 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.

arXiv comment10 pages, 3 figures, v2: two figures removed, sentences modified, title changed, to appear in PTEP letter

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• Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory
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