Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories

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 ν=2/(2m+1) are derived from deformations of the Wess-Zumino-Witten model 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 [25]. 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 as the low-energy effective theory for the periodic inverse-square t-J-V model.