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 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.

Final Version. Invited Article, for Special Issue of JSTAT on "Quantum Entanglement in Condensed Matter Physics"

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Cited by in corpus (16)

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• Entanglement equipartition in critical random spin chains
• Full counting statistics in the Haldane-Shastry chain
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Electron waiting times in coherent conductors are correlated
• Cornering the universal shape of fluctuations
• Equipartition of Entanglement in Quantum Hall States
• Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect
• Entanglement entropy in dynamic quantum-coherent conductors
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Entanglement entropy for integer quantum Hall effect in two and higher dimensions
• Bipartite Fluctuations of Critical Fermi Surfaces
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Absence of gapless Majorana edge modes in few-leg bosonic flux ladders