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Phys Rev Lett. 2013 Jun 7;110(23):235301. Epub 2013 Jun 4.

Super Efimov effect of resonantly interacting fermions in two dimensions.

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Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Department of Physics, University of Washington, Seattle, Washington 98195, USA.
Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA.


We study a system of spinless fermions in two dimensions with a short-range interaction fine-tuned to a p-wave resonance. We show that three such fermions form an infinite tower of bound states of orbital angular momentum ℓ=±1 and their binding energies obey a universal doubly exponential scaling E(3)((n))∝exp(-2e(3πn/4+θ)) at large n. This "super Efimov effect" is found by a renormalization group analysis and confirmed by solving the bound state problem. We also provide an indication that there are ℓ=±2 four-body resonances associated with every three-body bound state at E(4)((n))∝exp(-2e(3πn/4+θ-0.188)). These universal few-body states may be observed in ultracold atom experiments and should be taken into account in future many-body studies of the system.

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