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

TL;DR

This paper introduces a novel functional-renormalization-group aided density-functional theory (FRG-DFT) that effectively describes both ground and excited states of a one-dimensional nuclear matter system, capturing key spectral features.

Contribution

The work demonstrates for the first time that FRG-DFT can accurately describe excited states and spectral functions in a 1D nuclear matter system, unifying ground and excited state analysis.

Findings

FRG-DFT reproduces the spectral edge singularity of the density--density spectral function.

The method successfully describes the characteristic features of excited states in 1D nuclear matter.

The spectral function exhibits a singularity at the edge, consistent with Tomonaga-Luttinger liquid behavior.

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.