Unravelling the Li-Haldane Conjecture with the Projected Ensemble

Abstract:The entanglement spectra of fractional quantum Hall states contain universal fingerprints of their underlying topological order, as posited by the Li-Haldane conjecture. In this work, we uncover a finer universal structure within the entanglement spectra unravelled by projective measurements. Concretely, we study the projected ensemble of fractional quantum Hall states, defined as the collection of quantum states on a subsystem conditioned on measurement outcomes of its complement. We find that this ensemble exhibits a hidden hierarchy inside the Li-Haldane edge manifold: by conditioning on measurement outcomes, the entanglement spectrum's support is split into measurement-dependent sectors whose ranks we demonstrate are fixed by conformal field theory counting, an observation we dub the measurement-resolved Li-Haldane conjecture. For the non-Abelian Moore-Read state, this hierarchy is particularly rich: each parity-resolved edge manifold contains internal subspaces whose dimensions reproduce the conformal field theory counting of the opposite-parity sector. This structure persists even in realistic Coulomb-interacting ground states, establishing the projected ensemble as a sharp new probe of topological order beyond what the entanglement spectrum alone can detect.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2609.03833 [cond-mat.mes-hall]

(or arXiv:2609.03833v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2609.03833 Focus to learn more arXiv-issued DOI via DataCite

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