Local and Non-local Entanglement Witnesses of Fermi Liquid

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.