Effective-interaction approach to the many-boson problem

Abstract

We show that the convergence behavior of the many-body numerical diagonalization scheme for strongly interacting bosons in a trap can be significantly improved by the Lee-Suzuki method adapted from nuclear physics: One can construct an effective interaction that acts in a space much smaller than the original Hilbert space. In particular for short-ranged forces and strong correlations, the method offers a good estimate of the energy and the excitation spectrum, at a computational cost several orders of magnitude smaller than that required by the standard method.

5 pages, 4 figures

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• Analytic Harmonic Approach to the N-body problem
• Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions
• Many-Body Quantum Dynamics in the Decay of Bent Dark Solitons of Bose-Einstein Condensates
• Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions
• Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation
• Three interacting atoms in a one-dimensional trap: A benchmark system for computational approaches
• The $s$-wave scattering length of a Gaussian potential
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• Graphical Method for Effective Interaction with a New Vertex Function
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• Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap
• Eliminating the wave function singularity for ultracold atoms by similarity transformation
• Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach
• Enhanced many-body effects in the excitation spectrum of a weakly-interacting rotating Bose-Einstein condensate
• On the renormalization of contact interactions for the configuration-interaction method in two dimensions
• Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction
• Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance
• Fermionic properties of two interacting bosons in a two-dimensional harmonic trap
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• Ground and Low-Lying Collective States of Rotating Three-Boson System
• Roton in a few-body dipolar system
• Vortex patterns in moderately rotating Bose-condensed gas
• Formulation of effective interaction in terms of renormalized vertices and propagators
• Interference of longitudinal and transversal fragmentations in the Josephson tunneling dynamics of Bose-Einstein condensates
• Spatially partitioned many-body vortices
• Ground state properties of trapped boson system with finite-range Gaussian repulsion: Exact diagonalization study
• Novel phases in rotating Bose-condensed gas: vortices and quantum correlation
• Two-dimensional bosonic droplets in a harmonic trap
• The ab initio no-core shell model