  The bound state of \nuclide[6][\Lambda\Lambda]{He} is studied as a three-body
($\Lambda\Lambda\alpha$) system in a cluster effective field theory at leading
order (LO). We find that the system exhibits the limit cycle which is
associated with the formation of bound states called the Efimov states. This
implies that the three-body contact interaction should be promoted to LO. The
relationship of the binding energy and the $\Lambda\Lambda$ scattering length
is discussed as well as the role of the scale in this system.
