  Mechanical strain can generate a pseudo-magnetic field, and hence Landau
levels (LL), for low energy excitations of quantum matter in two dimensions. We
study the collective state of the fractionalised Majorana fermions arising from
residual generic spin interactions in the central LL, where the projected
Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and
particle-hole symmetries forbid any bilinear couplings, leading to an
intrinsically strongly interacting system; also, they allow the definition of a
filling fraction, which is fixed at 1/2. We argue that the resulting many-body
state is gapless within our numerical accuracy, implying ultra-short-ranged
spin correlations, while chirality correlators decay algebraically. This
amounts to a Kitaev `non-Fermi' spin liquid, and shows that interacting
Majorana Fermions can exhibit intricate behaviour akin to fractional quantum
Hall physics in an insulating magnet.
