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

• Published in: Progress of theoretical and experimental physics Vol. 2019; no. 1
• Main Authors: Yokota, Takeru, Yoshida, Kenichi, Kunihiro, Teiji
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.01.2019
• Subjects: Energy; Maximum entropy method; Physics; Quantum field theory; B32; D10; A63
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/pty139

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 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.