Universal dimer-dimer scattering in lattice effective field theory

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.