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.
Highlights
Consider a two-dimensional gapped system prepared in a pure state ρ partitioned into region A and its complement B
A physical consequence of this is the appearance of edge states at their boundaries [8], that can be used as a means to identify topological phases theoretically [9,10] or in the laboratory [11]
Spectrum [13], virtual entanglement edge states are witnessed in the spectrum of ρA in topological phases
Summary
Consider a two-dimensional gapped system prepared in a pure state ρ partitioned into region A and its complement B. We define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. Spectrum [13], virtual entanglement edge states are witnessed in the spectrum of ρA in topological phases.
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