Local density of states and particle entanglement in topological quantum fluids

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.

14 pages, 8 figures

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Cited by in corpus (8)

• STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• One-particle entanglement for one dimensional spinless fermions after an interaction quantum quench
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• A Scaling Function for the Particle Entanglement Entropy of Fermions
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States