Parton states as unique ground states of frustration free quantum Hall Hamiltonians with Fibonacci anyon excitations

We develop a general formalism to systematically derive frustration-free fractional quantum Hall (FQH) Hamiltonians in the presence of Landau level (LL) mixing. Their ground state correlations organize according to entangled Pauli principles, encoding the fluid’s DNA and, dictating the fractional nature of the statistics of their topological excitations. As we will show, the densest ground state - conjectured to be an incompressible quantum liquid - can be uniquely associated to a certain (closed-shell) parton state. Using S-duality, we show that for the case of 4 LLs, excitations of a filling fraction 2/3 liquid admit non-Abelian statistics and correspond to Fibonacci anyons.