Magnetic excitations, non-classicality and quantum wake spin dynamics in the Hubbard chain

Recent works have demonstrated that quantum Fisher information (QFI), a witness of multipartite entanglement, and magnetic Van Hove correlations G(r,t), a probe of local real-space real-time spin dynamics, can be extracted from inelastic neutron scattering on spin systems through accurate measurements of the dynamical spin structure factor S(k,ω). Here we apply theoretically these ideas to a fermionic system: the half-filled Hubbard chain with nearest-neighbor hopping. We use DMRG to find S(k,ω), from which QFI and G(r,t) are calculated. The QFI grows with U and can, with realistic energy resolution, witness bipartite entanglement at U≥2.5 (in units of hopping), where it also changes slope. This point is proximate to slope changes of the bandwidth W(U) and half-chain entanglement entropy. The G(r,t) results indicate a crossover in the short-time short-distance dynamics at low U characterized by ferromagnetic lightcone wavefronts, to a Heisenberg-like “quantum spin wake” behavior at large U featuring antiferromagnetic lightcones and spatially period-doubled antiferromagnetism. We find this crossover has largely been completed by U=3. Our results thus provide evidence that, in several aspects, the strong-coupling limit of the Hubbard chain is reached qualitatively already at a relatively modest interaction strength.