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

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T1 - On the renormalization of contact interactions for the configuration-interaction method in two-dimensions

AU - Rontani, Massimo

AU - Eriksson, G.

AU - Åberg, S.

AU - Reimann, S. M.

PY - 2017/3/7

Y1 - 2017/3/7

N2 - 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.

AB - 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.

KW - configuration interaction method

KW - degenerate Bose gases

KW - degenerate Fermi gases

KW - exact diagonalization

KW - Fermi pseudopotential

KW - few-body physics

KW - two-dimensional harmonic trap

UR - http://www.scopus.com/inward/record.url?scp=85015049270&partnerID=8YFLogxK

U2 - 10.1088/1361-6455/aa606a

DO - 10.1088/1361-6455/aa606a

M3 - Article

VL - 50

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 6

M1 - 065301

ER -