Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond

The Read-Rezayi (RR) parafermion states form a series of exotic non-Abelian fractional quantum Hall (FQH) states at filling ν=k/(k+2). Computationally, the wave functions of these states are prohibitively expensive to generate for large systems. We introduce a series of parton states, denoted 2̄ᵏ1ᵏ⁺¹, and show that they lie in the same universality classes as the particle-hole-conjugate RR (``anti-RR'') states. Our analytical results imply that a [U(1)ₖ₊₁×U(2k)_-1]/[SU(k)_-2×U(1)_-1] coset conformal field theory describes the edge excitations of the 2̄ᵏ1ᵏ⁺¹ state, suggesting nontrivial dualities with respect to previously known descriptions. The parton construction allows wave functions in anti-RR phases to be generated for hundreds of particles. We further propose the parton sequence n̄2̄²1⁴, with $n=1,2,3$, to describe the FQH states observed at ν=2+1/2, $2+2/5$, and $2+3/8$.