Descendant Fractional Quantum Hall States in the Chiral Z_p Toric Code

Quasiparticles offer a general platform for describing the properties of complex solid-state systems. In Kitaev's toric code model, excitations behave as electric and magnetic charges. We show that this quasiparticle picture holds at a deeper level by demonstrating that defects of the star operator—interpreted as electric charges—form fractional quantum Hall states in the chiral Z_p version of the model. In the solvable limit, the topologically ordered ground states are separated by sharp first-order transitions. Introducing a perturbation that induces dynamics in the electric charge variables broadens these transitions and gives rise to novel compressible and incompressible phases. These intermediate phases can be understood within a perturbative ansatz, where the model maps onto a number-conserving Bosonic Hofstadter problem, which is known for hosting superfluid and fractional Hall states. Despite the presence of higher-order, non-number-conserving corrections, our results indicate that the quasiparticle description in the toric code extends to a more fundamental level, where defects of the star operators form topologically ordered Hall states.