Local density of states and particle entanglement in topological quantum fluids

The understanding of particle entanglement is an important goal in the

studies of correlated quantum matter. The widely-used method of scanning

tunneling spectroscopy -- which measures the local density of states (LDOS) of

a many-body system by injecting or removing an electron from it -- is expected

to be sensitive to particle entanglement. In this paper, we systematically

investigate the relation between the particle entanglement spectrum (PES) and

the LDOS of fractional quantum Hall (FQH) states, the paradigmatic

strongly-correlated phases of electrons with topological order. Using exact

diagonalization, we show that the counting of levels in both the LDOS and PES

in the Jain sequence of FQH states can be predicted from the composite fermion

theory. We point out the differences between LDOS and PES characterization of

the bulk quasihole excitations, and we discuss the conditions under which the

LDOS counting can be mapped to that of PES. Our results affirm that tunneling

spectroscopy is a sensitive tool for identifying the nature of FQH states.