Entanglement in the Hubbard model

We demonstrate an enhancement of the quantum Fisher information, an established witness of multipartite entanglement, in the pseudogap regime of the Hubbard model and in cuprate experiments [1]. As for theory, we employ the dynamical vertex approximation (DΓA) [2], a non-local extension of dynamical mean-field theory. The pseudogap, characterized by a partially gapped electronic state, emerges near the superconducting transition in cuprate and nickelate materials, and DΓA properly describes it through the Hubbard model. The enhanced entanglement further motivates us to study bi-partite entanglement in the Hubbard model. To this end, we compute the two-site reduced density matrix within the DΓA framework [3], providing insight into the spatial structure of entanglement in strongly correlated electron systems [4].

[1] Bippus et al., Phys. Rev. B 112, L081110 (2025);  [2] Rohringer et al., Rev. Mod. Phys., 90, 025003 (2018); [3] Roósz et al., Phys. Rev. B, 110, 075115 (2024)  [4] Bippus et al., arXiv:2506.09780 (2025)