Local and Non-local Entanglement Witnesses of Fermi Liquid

TL;DR

This paper investigates how local and non-local operators can serve as entanglement witnesses in Fermi liquids, revealing that non-local operators can detect multipartite entanglement, thus offering new experimental tools for quantum material analysis.

Contribution

It demonstrates that non-local many-body operators can witness multipartite entanglement in Fermi liquids, unlike local operators, providing new methods to probe entanglement in quantum materials.

Findings

Local operators do not witness multipartite entanglement in Fermi liquids.

Non-local many-body operators can witness multipartite entanglement.

Results suggest new experimental approaches to detect entanglement depth.

Abstract

There is a growing interest both in utilizing entanglement means to characterize many-body systems and in uncovering their entanglement depth. Motivated by recent findings that the spin quantum Fisher information witnesses amplified multipartite entanglement of strange metals and characterizes their loss of quasiparticles, we study the quantum Fisher information in various cases of Fermi liquid. We show that local operators generically do not witness any multipartite entanglement in a Fermi liquid, but non-local many-body operators do. Our results point to novel experimental means to detect the entanglement depth of metallic fermionic systems and, in general, open a new avenue to the emerging exploration of entanglement in quantum materials.