  We introduce a family of many-body quantum states that describe interacting
spin one-half hard-core particles with bosonic or fermionic statistics on
arbitrary one- and two-dimensional lattices. The wave functions at lattice
filling fraction $\nu=2/(2m+1)$ are derived from deformations of the
Wess-Zumino-Witten model $\mathfrak{su}(3)_1$ and are related to the
$(m+1,m+1,m)$ Halperin fractional quantum Hall states. We derive long-range
SU(2) invariant parent Hamiltonians for these states which in two dimensions
are chiral $t$-$J$-$V$ models with additional three-body interaction terms. In
one dimension we obtain a generalisation to open chains of a periodic
inverse-square $t$-$J$-$V$ model proposed in [Z. N. C. Ha and F. D. M. Haldane,
Phys. Rev. B $\mathbf{46}$, 9359 (1992)]. We observe that the gapless
low-energy spectrum of this model and its open-boundary generalisation can be
described by rapidity sets with the same generalised Pauli exclusion principle.
A two-component compactified free boson conformal field theory is identified
that has the same central charge and scaling dimensions as the periodic bosonic
inverse-square $t$-$J$-$V$ model.
