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On the renormalization of contact interactions for the configuration-interaction method in two-dimensions

Rontani, Massimo; Eriksson, G. LU ; Åberg, S. LU and Reimann, S. M. LU (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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Please use this url to cite or link to this publication:
author
organization
publishing date
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
publisher
IOP Publishing
external identifiers
  • scopus:85015049270
  • wos:000396176200001
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
2018-01-07 11:56:44
@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>},
  articleno    = {065301},
  author       = {Rontani, Massimo and Eriksson, G. and Åberg, S. and Reimann, S. M.},
  issn         = {0953-4075},
  keyword      = {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},
  volume       = {50},
  year         = {2017},
}