  The Jordan-Wigner map in 2D is as an exact lattice regularization of the 2
pi-flux attachment to a hard-core boson (or spin-1/2) leading to a
composite-fermion particle. When the spin-1/2 model obeys ice rules this map
preserves locality, namely, local Rohkshar-Kivelson models of spins are mapped
onto local models of Jordan-Wigner/composite-fermions. Using this
composite-fermion dual representation of RK models, we construct spin-liquid
states by projecting Slater determinants onto the subspaces of the ice rules.
Interestingly, we find that these composite-fermions behave as ``dipolar"
partons for which the projective implementations of symmetries are very
different from standard ``point-like" partons. We construct interesting
examples of composite-fermion liquid states that respect all microscopic
symmetries of the RK model. In the six-vertex subspace, we constructed a
time-reversal and particle-hole-invariant state featuring two massless Dirac
nodes, which is a composite-fermion counterpart to the classic pi-flux state of
Abrikosov-Schwinger fermions in the square lattice. This state is a good ground
state candidate for a modified RK-like Hamiltonian of quantum spin-ice. In the
dimer subspace, we construct a state fearturing a composite Fermi surface but
with nesting instabilities towards ordered phases such as the columnar state.
We have also analyzed the low energy emergent gauge structure. If one ignores
confinement, the system would feature a U(1) x U(1) low energy gauge structure
with two associated gapless photon modes, but with the composite fermion
carrying gauge charge only for one photon and behaving as a gauge neutral
dipole under the other. These states are examples of pseudo-scalar U(1) spin
liquids where mirror and time-reversal symmetries act as particle-hole
conjugations, and the emergent magnetic fields are even under such
time-reversal or lattice mirror symmetries.
