Entanglement Chern number for an extensive partition of a topological ground state

Abstract

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an entanglement Chern number as a useful, natural, and calculable topological invariant, which is potentially relevant to various topological ground states. We show that it serves as an alternative topological invariant for time-reversal invariant systems and as a new topological invariant for a weak topological phase of a superlattice Wilson-Dirac model. In principle, the entanglement Chern number can also be effective for interacting systems such as topological insulators in contrast to $Z_2$ invariants.

4 pages, 2 figures, final version. (Open Access)

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Cited by in corpus (8)

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• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Entanglement Chern number for three-dimensional topological insulators: Characterization by Weyl points of entanglement Hamiltonians
• Topological magnetoelectric pump in three dimensions
• Refined Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum