title: Diagnosing Topological Edge States via Entanglement Monogamy.
abstract: Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix. This matrix is often tractable either analytically or numerically, and it precisely captures the relevant correlations of the system. By invoking the concept of monogamy of entanglement, we show that highly entangled states supported across a system bipartition are largely disentangled from the rest of the system, thus, usually appearing as gapless edge states. We then define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. We demonstrate the versatility of this qualifier by applying it to various free and interacting fermionic topological systems.
authors.affiliation: School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
authors.forename: K
authors.initials: K
authors.lastname: Meichanetzidis
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: J
authors.initials: J
authors.lastname: Eisert
authors.affiliation: Interdisciplinary Theoretical Science Research Group (iTHES), RIKEN, Wako-shi, Saitama 351-0198, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Cirio
authors.affiliation: Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.
authors.forename: V
authors.initials: V
authors.lastname: Lahtinen
authors.affiliation: School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
authors.forename: J K
authors.initials: JK
authors.lastname: Pachos