Fluctuations and Entanglement spectrum in quantum Hall states

TL;DR

This paper explores the relationship between charge fluctuations and entanglement spectra in quantum Hall states, demonstrating how measurements of charge cumulants can reveal entanglement features in integer quantum Hall systems and discussing limitations in fractional cases.

Contribution

It establishes a link between bipartite charge fluctuations and entanglement spectra, providing a method to infer entanglement properties from charge measurements in quantum Hall states.

Findings

Entanglement spectrum features can be reproduced from second charge cumulant in integer quantum Hall states.

Free fermion relations do not generally extend to fractional quantum Hall states at ν=1/3.

Derived spectral functions for entanglement in quantum Hall edge states modeled as Luttinger liquids.

Abstract

The measurement of quantum entanglement in many-body systems remains challenging. One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of R\' enyi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies. In the case of the integer quantum Hall effect, we show that it is possible to reproduce the generic features of the entanglement spectrum from a measurement of the second charge cumulant only. Additionally, asking whether it is possible to extend the free fermion result to the $\nu=1/3$ fractional quantum Hall case, we provide numerical evidence that the answer is negative in general. We further address the problem of quantum Hall edge states described by a Luttinger liquid, and derive expressions for the spectral functions of the real space entanglement spectrum at a quantum point contact realized in a quantum Hall sample.