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

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.

Major revision accepted for publication in J. Phys. B: At. Mol. Phys

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• The $s$-wave scattering length of a Gaussian potential
• Eliminating the wave function singularity for ultracold atoms by similarity transformation
• Interaction blockade for bosons in an asymmetric double well
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• A simple variational quantum Monte Carlo-effective mass approach for excitons and trions in quantum dots
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• Few-to-many-particle crossover of pair excitations in a superfluid
• Inversion of coherent backscattering with interacting Bose-Einstein condensates in two-dimensional disorder : a Truncated Wigner approach
• When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases
• Effective two- and three-body interactions between dressed impurities in a tilted double-well potential
• Equivalence of dissipative and dissipationless dynamics of interacting quantum systems with its application to the unitary Fermi gas
• Vortices in the Many-Body Excited States of Interacting Bosons in Two Dimension