  The light double $\Lambda$ hypernuclei, ${}_{\Lambda\Lambda}^{\ \ 4}$H and
${}_{\Lambda\Lambda}^{\ \ 6}$He, are studied as three-body $\Lambda\Lambda d$
and $\Lambda\Lambda\alpha$ cluster systems in halo/cluster effective field
theory at leading order. We find that the $\Lambda\Lambda d$ system in spin-0
channel does not exhibit a limit cycle whereas the $\Lambda\Lambda d$ system in
spin-1 channel and the $\Lambda\Lambda\alpha$ system in spin-0 channel do. The
limit cycle is associated with the formation of bound states, known as Efimov
states, in the unitary limit. For the $\Lambda\Lambda d$ system in the spin-0
channel we estimate the scattering length $a_0$ for $S$-wave $\Lambda$
hyperon-hypertriton scattering as $a_0=16.0\pm 3.0$ fm. We also discuss that
studying the cutoff dependences in the $\Lambda\Lambda d$ and
$\Lambda\Lambda\alpha$ systems, the bound state of ${}_{\Lambda\Lambda}^{\ \
4}$H is not an Efimov state but formed due to a high energy mechanism whereas
that of ${}_{\Lambda\Lambda}^{\ \ 6}$He may be regarded as an Efimov state.
