Inner workings of fractional quantum Hall parent Hamiltonians: A matrix product state point of view

We study frustration-free Hamiltonians of fractional quantum Hall (FQH) states from the point view matrix product state (MPS) representation their ground and excited states. There is a wealth solvable models relating to FQH physics, which, however, mostly derived analyzed vantage first-quantized "analytic clustering properties". In contrast, one obtains long-ranged lattice when these are studied in an orbital basis, which natural basis for MPS The connection between MPS-like parent central guiding principle construction models, but thus far, only short-range MPSs finite bond dimension. situation context fundamentally different. Here we expose direct link infinite-bond-dimension structure Laughlin-conformal field theory (CFT) Hamiltonians. While focusing on Laughlin state, generalizations other CFT-MPSs will become transparent.