Fractional Quantum Hall Effect from Hilbert Space Algebra and New Approaches for Experimental Realisation

We show that model states of fractional quantum Hall (FQH) fluids for many topological phases can be uniquely determined by the Hilbert space algebra manifested as the classical reduced density matrix constraints, or the local exclusion constraint (LEC). The scheme allows us to identify filling factors, topological shifts and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. Elementary excitations of the FQH phases can also be characterised by the LECs. More interestingly, the LEC formalism leads to a new perspective for the FQH model Hamiltonians, which can now be understood as a the von Neumann lattice of local potentials. This suggests a completely new way of experimentally realising the FQH states, including the coveted non-Abelian states (e.g the Moore-Read and Fibonacci states). We show that by tuning the local one-body potential profile, one can effectively tune the individual pseudopotentials (not just two-body, but few-body pseudopotentials) independently, and this can be done in experiments in principle. (related arXiv papers: Bo Yang, arXiv: 1901.00047, Bo Yang, Ajit Balram, arXiv:1907.09493, Bo Yang, Ying-Hai Wu, Zlatko Papic, arXiv:1907.12572)