Local density of states and particle entanglement in topological quantum fluids

TL;DR

This paper explores how local density of states measurements via tunneling spectroscopy relate to particle entanglement in fractional quantum Hall states, showing that LDOS can reveal topological order and quasihole excitations.

Contribution

It systematically analyzes the connection between LDOS and particle entanglement spectrum in FQH states, demonstrating the predictive power of composite fermion theory for level counting.

Findings

LDOS and PES level counting can be predicted by composite fermion theory.

Tunneling spectroscopy can identify the nature of FQH states.

Differences exist between LDOS and PES in characterizing quasihole excitations.

Abstract

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.