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

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.

37 pages, 7 figures

References in corpus (21)

• Exact evolution equation for the effective potential
• Chiral effective field theory and nuclear forces
• Improved nuclear matter calculations from chiral low-momentum interactions
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Recent developments in no-core shell-model calculations
• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Three-body forces: From cold atoms to nuclei
• Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-$\alpha$ Scattering, and Neutron Matter
• Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter
• An exactly solvable model of the BCS-BEC crossover
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Phase space deformation of a trapped dipolar Fermi gas
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Implementation and pre-optimization
• Non-empirical pairing functional
• Density Functional Theory for a Confined Fermi System with Short-Range Interaction
• Ab Initio Derivation of Model Energy Density Functionals
• Two-particle irreducible functional renormalization group schemes---a comparative study
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Similarity Renormalization Group Evolution of Many-Body Forces in a One-Dimensional Model
• UNEDF: Advanced Scientific Computing Collaboration Transforms the Low-Energy Nuclear Many-Body Problem

Cited by in corpus (22)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Turning the nuclear energy density functional method into a proper effective field theory: reflections
• Functional Renormalization Group and Kohn-Sham scheme in Density Functional Theory
• Functional renormalization-group calculation of the equation of state of one-dimensional nuclear matter inspired by the Hohenberg--Kohn theorem
• Toward ab initio charge symmetry breaking in nuclear energy density functionals
• Ab-initio description of excited states of a one-dimensional nuclear matter with the Hohenberg-Kohn-theorem-inspired functional-renormalization-group method
• Functional-renormalization-group aided density-functional analysis for the correlation energy of the two-dimensional homogeneous electron gas
• Ab initio construction of the energy density functional for electron systems with the functional-renormalization-group-aided density functional theory
• Microscopic derivation of density functional theory for superfluid systems based on effective action formalism
• Functional-renormalization-group approach to classical liquids with short-range repulsion: a scheme without repulsive reference system
• Optimized nuclear energy density functionals including long-range pion contributions
• A complex Langevin approach to ultracold fermions
• KIDS density functional for deformed nuclei: Examples of the even-even Nd isotopes
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Construction of energy density functional for arbitrary spin polarization using functional renormalization group
• Physics-informed neural networks for solving functional renormalization group on a lattice
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Functional renormalization group for classical liquids without recourse to hard-core reference systems: A study of three-dimensional Lennard-Jones liquids