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

TL;DR

This paper addresses the divergence issues in the configuration interaction method for 2D contact interactions by introducing a renormalization scheme that yields cutoff-independent physical observables, demonstrated on ultracold atoms.

Contribution

It proposes a simple renormalization scheme for contact interactions in 2D CI calculations, enabling convergence and accurate physical predictions.

Findings

Renormalization removes divergence in 2D CI calculations.

The method achieves cutoff-independent few-body observables.

Application to ultracold atoms confirms effectiveness.

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.