Diagnosing Topological Edge States via Entanglement Monogamy

TL;DR

This paper introduces an entanglement-based method using the fermionic covariance matrix and monogamy of entanglement to identify topological edge states in fermionic systems, offering a new diagnostic tool.

Contribution

It proposes a novel entanglement qualifier based on the covariance matrix and monogamy principles to detect topological edge states in both free and interacting fermionic systems.

Findings

Successfully applied to various free fermionic topological systems.

Effective in identifying edge states through correlation patterns.

Applicable to interacting fermionic systems.

Abstract

Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this work, 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 bi-partition are largely disentangled from the rest of the system, thus appearing usually 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.