On the renormalization of contact interactions for the configuration-interaction method in two-dimensions
(2017) In Journal of Physics B: Atomic, Molecular and Optical Physics 50(6).- Abstract
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac δ-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schrödinger equation for a regularized contact interaction. We... (More)
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac δ-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schrödinger equation for a regularized contact interaction. We discuss here a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.
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- author
- Rontani, Massimo ; Eriksson, G. LU ; Åberg, S. LU and Reimann, S. M. LU
- organization
- publishing date
- 2017-03-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- configuration interaction method, degenerate Bose gases, degenerate Fermi gases, exact diagonalization, Fermi pseudopotential, few-body physics, two-dimensional harmonic trap
- in
- Journal of Physics B: Atomic, Molecular and Optical Physics
- volume
- 50
- issue
- 6
- article number
- 065301
- publisher
- IOP Publishing
- external identifiers
-
- wos:000396176200001
- scopus:85015049270
- ISSN
- 0953-4075
- DOI
- 10.1088/1361-6455/aa606a
- language
- English
- LU publication?
- yes
- id
- 31934167-5122-40d2-aee1-438962e908fb
- date added to LUP
- 2017-03-23 09:41:05
- date last changed
- 2025-10-14 13:08:45
@article{31934167-5122-40d2-aee1-438962e908fb,
abstract = {{<p>The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac δ-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schrödinger equation for a regularized contact interaction. We discuss here a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.</p>}},
author = {{Rontani, Massimo and Eriksson, G. and Åberg, S. and Reimann, S. M.}},
issn = {{0953-4075}},
keywords = {{configuration interaction method; degenerate Bose gases; degenerate Fermi gases; exact diagonalization; Fermi pseudopotential; few-body physics; two-dimensional harmonic trap}},
language = {{eng}},
month = {{03}},
number = {{6}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics B: Atomic, Molecular and Optical Physics}},
title = {{On the renormalization of contact interactions for the configuration-interaction method in two-dimensions}},
url = {{http://dx.doi.org/10.1088/1361-6455/aa606a}},
doi = {{10.1088/1361-6455/aa606a}},
volume = {{50}},
year = {{2017}},
}