Renormalization group study of the four-body problem

Abstract

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.

11 pages, 6 figures; v2: revised and published version

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• Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length
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• Efimov physics in heteronuclear four-body systems
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• Convergence of a renormalization group approach to dimer-dimer scattering
• Universality in Four-Boson Systems
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• Efimov physics from the functional renormalization group
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• Topological origin of universal few-body clusters in Efimov physics
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• Dimer-atom-atom recombination in the universal four-boson system
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• Efimov-like physics in fraction-dimensional Bose systems with three-body interaction
• Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions