Local density of states and particle entanglement in topological quantum fluids

The understanding of particle entanglement is an important goal in the studies correlated quantum matter. widely used method scanning tunneling spectroscopy---which measures local density states (LDOS) a many-body system by injecting or removing electron from it---is expected to be sensitive entanglement. In this paper, we systematically investigate relation between spectrum (PES) and LDOS fractional Hall (FQH) states, paradigmatic strongly phases electrons with topological order. Using exact diagonalization, show that counting levels both PES Jain sequence FQH can predicted composite fermion theory. We point out differences characterization bulk quasihole excitations, discuss conditions under which mapped PES. Our results affirm spectroscopy tool for identifying nature states.