Simplification of exact parent Hamiltonians while preserving topological order

Determine how far the exact parent Hamiltonians for lattice-sampled continuum lowest-Landau-level fractional quantum Hall states can be simplified toward experimentally accessible models while preserving the topological order of their target states.

Background

The paper constructs Hermitian lattice parent Hamiltonians whose exact zero modes are continuum lowest-Landau-level model states sampled on lattice sites. These Hamiltonians provide exact reference manifolds for Laughlin, Moore–Read, and Fibonacci states, but their interaction terms can involve higher-body or otherwise experimentally demanding operators.

The numerical results show that simpler interactions can approximate some target manifolds: short-range density interactions stabilize Laughlin states, and two-body onsite repulsion supports a Moore–Read triplet within an isolated lattice band. However, the Moore–Read manifold becomes spectrally less isolated and undergoes a level crossing when interband mixing grows, while the Fibonacci benchmarks exhibit substantial finite-size and interaction-dependent limitations. The unresolved problem is therefore to identify the extent to which exact parent-Hamiltonian interactions can be reduced to experimentally realistic models without destroying the target topological order.