Clifford-invariant additive measure for fermionic correlations

Quantifying correlations in many-body systems can be crucial for the analysis and approximate simulations of condensed matter systems. As a prominent example, entanglement entropy has useful scaling properties and forms the basis for tensor network methods. Entanglement measures for fermionic systems, however, are highly sensitive to Clifford (single-particle) rotations, even though these do not contain any quantum complexity. To address this issue, we introduce an explicit measure for fermionic correlations related to the Plucker identities that we dub Plucker entropy. This measure is invariant with respect to Clifford rotations and obeys additivity, giving rise to entropy-like scaling properties. We study Plucker entropy numerically as applied to the low-energy physics of the Hubbard model, capturing the absence of correlations both in its free fermion and its Mott insulator regimes. Furthermore, we analyze Plucker entropy as a resource for fermionic Clifford computations ("quantum magic"). Inspired by the connection between entanglement entropy and tensor networks, potential applications to approximate classical methods are discussed.