Snapshot-based detection of hidden off-diagonal long range order in fractional quantum hall states on lattices

Revealing the existence of hidden off-diagonal long range order is believed to be a promising avenue towards identifying and characterizing topological order. In continuum fractional quantum Hall systems this can be accomplished by attaching gauge flux tubes onto the particles. Following the recent advances of cold atom experiments in optical lattices, probing this hidden, non-local order parameter with Fock-basis snapshots for lattice analogs is now within reach. Here, we demonstrate the existence of hidden off-diagonal long range order in quasi two-dimensional lattices in the ν=1/2-groundstate of the experimentally realistic isotropic Hofstadter-Bose-Hubbard model. To this end, we provide a MPS-driven, hybrid one and two-site snapshot procedure to sample the one-particle reduced density matrix and all particle positions simultaneously, emulating an experimentally feasible protocol. We present strong numerical indications for the emergence of an algebraic decay and discuss the resolution achievable using only few snapshots.