Boundary-locality and perturbative structure of entanglement spectra in gapped systems

Abstract

The entanglement between two parts of a many-body system can be characterized in detail by the entanglement spectrum. Focusing on gapped phases of one-dimensional systems, we show how this spectrum is dominated by contributions from the boundary between the parts. This contradicts the view of an "entanglement Hamiltonian" as a bulk entity. The boundary-local nature of the entanglement spectrum is clarified through its hierarchical level structure, through the combination of two single-boundary spectra to form a two-boundary spectrum, and finally through consideration of dominant eigenfunctions of the entanglement Hamiltonian. We use the boundary-locality to formulate a perturbative scheme for calculating entanglement spectra.

4 pages, 3 figures; supplementary material added (6 pages, 2 figures); minor revisions to match the published version in Physical Review Letters

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