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

TL;DR

This paper demonstrates that in gapped one-dimensional systems, the entanglement spectrum is primarily determined by boundary contributions, challenging the bulk-centric view and enabling a boundary-based perturbative calculation approach.

Contribution

It reveals the boundary-local nature of entanglement spectra in gapped systems and introduces a perturbative scheme for their calculation based on this locality.

Findings

Entanglement spectrum dominated by boundary contributions.

Hierarchical structure of entanglement levels explained.

Perturbative method for spectrum calculation developed.

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.