  We construct large classes of exactly solvable pseudo-Hermitian 2D spin
Hamiltonians. The ground states of these systems depend only on the spatial
topology of the system. We identify the ground state system on a surface with
the value assigned to the surface by a non-semisimple TQFT generalizing the
Turaev-Viro model. A non-trivial example arises from a non-semisimple
subcategory of representations of quantum sl(2) where the quantum parameter is
specialized to a root of unity.
