Formation of Selfbound States in a One-Dimensional Nuclear Model -- A Renormalization Group based Density Functional Study

TL;DR

This paper combines Density Functional Theory and Renormalization Group techniques to study selfbound many-body systems in one dimension, providing insights into microscopic interactions and energy functionals relevant for nuclear physics.

Contribution

It introduces a novel DFT-RG approach to connect microscopic nuclear forces with density functionals, enabling analysis of ground and excited states in one-dimensional fermionic systems.

Findings

Computed ground-state energies and densities for 1D fermion systems.

Demonstrated extraction of excited state energies from correlation functions.

Discussed control of fermion self-interactions in DFT studies.

Abstract

In nuclear physics, Density Functional Theory (DFT) provides the basis for state-of-the art studies of ground-state properties of heavy nuclei. However, the direct relation of the density functional underlying these calculations and the microscopic nuclear forces is not yet fully understood. We present a combination of DFT and Renormalization Group (RG) techniques which allows to study selfbound many-body systems from microscopic interactions. We discuss its application with the aid of systems of identical fermions interacting via a long-range attractive and short-range repulsive two-body force in one dimension. We compute ground-state energies, intrinsic densities, and density correlation functions of these systems and compare our results to those obtained from other methods. In particular, we show how energies of excited states as well as the absolute square of the ground-state wave function can be extracted from the correlation functions within our approach. The relation between many-body perturbation theory and our DFT-RG approach is discussed and illustrated with the aid of the calculation of the second-order energy correction for a system of $N$ identical fermions interacting via a general two-body interaction. Moreover, we discuss the control of spuriously emerging fermion self-interactions in DFT studies within our framework. In general, our approach may help to guide the development of energy functionals for future quantitative DFT studies of heavy nuclei from microscopic interactions.