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The understanding of particle entanglement is an important goal in thestudies of correlated quantum matter. The widely-used method of scanningtunneling spectroscopy -- which measures the local density of states (LDOS) ofa many-body system by injecting or removing an electron from it -- is expectedto be sensitive to particle entanglement. In this paper, we systematicallyinvestigate the relation between the particle entanglement spectrum (PES) andthe LDOS of fractional quantum Hall (FQH) states, the paradigmaticstrongly-correlated phases of electrons with topological order. Using exactdiagonalization, we show that the counting of levels in both the LDOS and PESin the Jain sequence of FQH states can be predicted from the composite fermiontheory. We point out the differences between LDOS and PES characterization ofthe bulk quasihole excitations, and we discuss the conditions under which theLDOS counting can be mapped to that of PES. Our results affirm that tunnelingspectroscopy is a sensitive tool for identifying the nature of FQH states.

Local density of states and particle entanglement in topological quantum fluids