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

TY - JOUR

T1 - Comparison of renormalized interactions using one-dimensional few-body systems as a testbed

AU - Brauneis, Fabian

AU - Hammer, Hans Werner

AU - Reimann, Stephanie M.

AU - Volosniev, Artem G.

N1 - Publisher Copyright: © 2025 American Physical Society.

PY - 2025/1

Y1 - 2025/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85214288947&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.111.013303

DO - 10.1103/PhysRevA.111.013303

M3 - Journal article

AN - SCOPUS:85214288947

SN - 2469-9926

VL - 111

JO - Physical Review A

JF - Physical Review A

IS - 1

M1 - 013303

ER -