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arXiv · 1107.1726

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

Vincenzo Alba·Masudul Haque·Andreas M. Laeuchli
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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.

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Vincenzo Alba, Masudul Haque, Andreas M. Laeuchli. 2011-07-08. Boundary-locality and perturbative structure of entanglement spectra in gapped systems. https://doi.org/10.1103/physrevlett.108.227201

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