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arXiv · 0810.4305

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

M. Rontani·G. Eriksson·S. Åberg·S. M. Reimann
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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 delta-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 Schroedinger equation for a regularized contact interaction. We here discuss 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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M. Rontani, G. Eriksson, S. Åberg, S. M. Reimann. 2017-02-15. On the renormalization of contact interactions for the configuration-interaction method in two dimensions. https://doi.org/10.1088/1361-6455%2Faa606a

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