Comparison of renormalized interactions using one-dimensional few-body systems as a testbed

Abstract

Even though the one-dimensional contact interaction requires no regularization, renormalization methods have been shown to improve the convergence of numerical ab initio calculations considerably. In this work, we compare and contrast these methods: `the running coupling constant' where the two-body ground state energy is used as a renormalization condition, and two effective interaction approaches that include information about the ground as well as excited states. In particular, we calculate the energies and densities of few-fermion systems in a harmonic oscillator with the configuration interaction method, and compare the results based upon renormalized and bare interactions. We find that the use of the running coupling constant instead of the bare interaction improves convergence significantly. A comparison with an effective interaction, which is designed to reproduce the relative part of the energy spectrum of two particles, showed a similar improvement. The effective interaction provides an additional improvement if the center-of-mass excitations are included in the construction. Finally, we discuss the transformation of observables alongside the renormalization of the potential, and demonstrate that this might be an essential ingredient for accurate numerical calculations.

Version accepted for publication in Phys. Rev. A

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• Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose-Bose-Bose mixtures
• Two-dimensional bosonic droplets in a harmonic trap
• Effective two- and three-body interactions between dressed impurities in a tilted double-well potential
• From spontaneous to explicit symmetry breaking in a finite-sized system: Bosonic bound states of an impurity
• Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions