Four-Boson Continuous Scale Symmetry Breaking

We show that the homogeneous Faddeev-Yakubovski formalism for the bound state of four identical bosons with zero-range interaction in the unitary limit (infinite two-body scattering length) presents scale invariance in the ultraviolet (UV) region. By resorting to an approximate form of the integral equations in the UV limit (considering exclusively an attractive pairwise zero-range interaction), we demonstrate that a pair of log-periodic solutions, with a cycle distinct from the three-boson one, exists with a four-body scale required to define the phase between them.