Fluctuations and entanglement spectrum in quantum Hall states

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 Rényi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, through the Rényi 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 cum..