Renormalization group study of the four-body problem

Details Renormalization group study of the four-body problem Renormalization group study of the four-body problem

2009-10-23

arxiv.org/abs/0910.4586v2

Phys. Rev. A 81, 052709 (2010)

Physics

Condensed Matter

Quantum Gases

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

Scientific paper

10.1103/PhysRevA.81.052709

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.

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