Kagomé Lattice Antiferromagnet Stripped to Its Basics

We study a model of a spin S = 1/2 Heisenberg antiferromagnet on a one dimensional lattice with the local symmetry of the two dimensional kagom{\'e} lattice. Using three complementary approaches, it is shown that the low energy spectrum can be described by two critical Ising models with different velocities. One of these velocities is small, leading to a strongly localized Majorana fermion. These excitations are singlet ones whereas the triplet sector has a spectral gap.