  Light hypernuclei with an $\alpha$ cluster substructure of the core nucleus
are studied using an accurate cluster approach (the Hyper-THSR wave function)
in combination with a density-dependent $\Lambda$ hyperon-nuclear interaction
derived from chiral SU(3) effective field theory. This interaction includes
important two-pion exchange processes involving $\Sigma N$ intermediate states
and associated three-body mechanisms as well as effective mass and surface
terms arising in a derivative expansion of the in-medium $\Lambda$ self-energy.
Applications and calculated results are presented and discussed for
$_\Lambda^9$Be and $^{13}_\Lambda$C. Furthermore, the result of the lightest
$\alpha$ clustered hypernucleus, $^5_{\Lambda}$He using realistic $ab initio$
four nucleon density is shown.
