Universal dimer-dimer scattering in lattice effective field theory

Abstract

We consider two-component fermions with short-range interactions and large scattering length. This system has universal properties that are realized in several different fields of physics. In the limit of large fermion-fermion scattering length $a_{\mathrm{ff}}$ and zero-range interaction, all properties of the system scale proportionally with $a_{\mathrm{ff}}$. For the case with shallow bound dimers, we calculate the dimer-dimer scattering phase shifts using lattice effective field theory. We extract the universal dimer-dimer scattering length $a_{\mathrm{dd}}/a_{\mathrm{ff}}=0.618(30)$ and effective range $r_{\mathrm{dd}}/a_{\mathrm{ff}}=-0.431(48)$. This result for the effective range is the first calculation with quantified and controlled systematic errors. We also benchmark our methods by computing the fermion-dimer scattering parameters and testing some predictions of conformal scaling of irrelevant operators near the unitarity limit.

15 pages, 6 figures, version accepted for publication in Phys. Lett. B

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• Breaking and restoration of rotational symmetry in the low-energy spectrum of light alpha-conjugate nuclei on the lattice I: ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$
• Effective forces between quantum bound states
• Universality in fermionic dimer-dimer scattering
• Lattice Improvement in Lattice Effective Field Theory
• Searching for the Tetraneutron Resonance on the Lattice
• Coboson many-body formalism for atom-dimer scattering length
• Recombination in the universal four-fermion system