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Comparison of renormalized interactions using one-dimensional few-body systems as a testbed

Brauneis, Fabian ; Hammer, Hans Werner ; Reimann, Stephanie M. LU and Volosniev, Artem G. (2025) In Physical Review A 111(1).
Abstract

Even though the one-dimensional contact interaction requires no regularization, renormalization methods have been shown to improve the convergence of numerical calculations considerably. In this work, we compare and contrast these methods: "the running coupling constant"where the two-body ground-state energy is used as a renormalization condition, and two effective interaction approaches that include information about the ground as well as excited states. In particular, we calculate the energies and densities of few-fermion systems in a harmonic oscillator with the configuration-interaction method and compare the results based upon renormalized and bare interactions. We find that the use of the running coupling constant instead of the... (More)

Even though the one-dimensional contact interaction requires no regularization, renormalization methods have been shown to improve the convergence of numerical calculations considerably. In this work, we compare and contrast these methods: "the running coupling constant"where the two-body ground-state energy is used as a renormalization condition, and two effective interaction approaches that include information about the ground as well as excited states. In particular, we calculate the energies and densities of few-fermion systems in a harmonic oscillator with the configuration-interaction method and compare the results based upon renormalized and bare interactions. We find that the use of the running coupling constant instead of the bare interaction improves convergence significantly. A comparison with an effective interaction, which is designed to reproduce the relative part of the energy spectrum of two particles, showed a similar improvement. The effective interaction provides an additional improvement if the center-of-mass excitations are included in the construction. Finally, we discuss the transformation of observables alongside the renormalization of the potential, and demonstrate that this might be an essential ingredient for accurate numerical calculations.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review A
volume
111
issue
1
article number
013303
publisher
American Physical Society
external identifiers
  • scopus:85214288947
ISSN
2469-9926
DOI
10.1103/PhysRevA.111.013303
language
English
LU publication?
yes
id
aebd7e46-6247-4dcc-9be9-9b8d1fc9ed60
date added to LUP
2025-03-25 15:12:49
date last changed
2025-04-04 14:00:16
@article{aebd7e46-6247-4dcc-9be9-9b8d1fc9ed60,
  abstract     = {{<p>Even though the one-dimensional contact interaction requires no regularization, renormalization methods have been shown to improve the convergence of numerical calculations considerably. In this work, we compare and contrast these methods: "the running coupling constant"where the two-body ground-state energy is used as a renormalization condition, and two effective interaction approaches that include information about the ground as well as excited states. In particular, we calculate the energies and densities of few-fermion systems in a harmonic oscillator with the configuration-interaction method and compare the results based upon renormalized and bare interactions. We find that the use of the running coupling constant instead of the bare interaction improves convergence significantly. A comparison with an effective interaction, which is designed to reproduce the relative part of the energy spectrum of two particles, showed a similar improvement. The effective interaction provides an additional improvement if the center-of-mass excitations are included in the construction. Finally, we discuss the transformation of observables alongside the renormalization of the potential, and demonstrate that this might be an essential ingredient for accurate numerical calculations.</p>}},
  author       = {{Brauneis, Fabian and Hammer, Hans Werner and Reimann, Stephanie M. and Volosniev, Artem G.}},
  issn         = {{2469-9926}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review A}},
  title        = {{Comparison of renormalized interactions using one-dimensional few-body systems as a testbed}},
  url          = {{http://dx.doi.org/10.1103/PhysRevA.111.013303}},
  doi          = {{10.1103/PhysRevA.111.013303}},
  volume       = {{111}},
  year         = {{2025}},
}