  Half-integer quantized flux vortices appear in honeycomb lattices when the
signs of an odd number of couplings around a plaquette are inverted. We show
that states trapped at these vortices can be isolated by applying inhomogeneous
strain to the system. A vortex then results in localized mid-gap states lying
between the strain-induced pseudo-Landau levels, with $2n+1$ midgap states
appearing between the $n$th and the $n+1$st level. These states are
well-defined spectrally isolated and spatially localized excitations that could
be realized in electronic and photonic systems based on graphene-like honeycomb
lattices. In the context of Kitaev's honeycomb model of interacting spins, the
mechanism improves the localization of non-Abelian anyons in the spin-liquid
phase, and reduces their mutual interactions. The described states also serve
as a testbed for fundamental physics in the emerging low-energy theory, as the
correct energies and degeneracies of the excitations are only replicated if one
accounts for the effective hyperbolic geometric induced by the strain. We
further illuminate this by considering the effects of an additional external
magnetic field, resulting in a characteristic spatial dependence that directly
maps out the inhomogeneous metric of the emerging hyperbolic space.
