Magnetic excitations, nonclassicality, and quantum wake spin dynamics in the Hubbard chain

Abstract

Recent work has 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 successfully extracted from inelastic neutron scattering on spin systems through accurate measurements of the dynamical spin structure factor $S(k,\ensuremath{\omega})$. Here we apply theoretically these ideas to the half-filled Hubbard chain with nearest-neighbor hopping, away from the strong-coupling limit. This model has nontrivial redistribution of spectral weight in $S(k,\ensuremath{\omega})$ going from the noninteracting limit ($U=0$) to strong coupling ($U\ensuremath{\rightarrow}\ensuremath{\infty}$), where it reduces to the Heisenberg quantum spin chain. We use the density matrix renormalization group to find $S(k,\ensuremath{\omega})$, from which QFI is then calculated. We find that QFI grows with $U$. With realistic energy resolution it becomes capable of witnessing bipartite entanglement above $U=2.5$ (in units of the hopping), where it also changes slope. This point is also proximate to slope changes of the bandwidth $W(U)$ and the half-chain von Neumann entanglement entropy. We compute $G(r,t)$ by Fourier transforming $S(k,\ensuremath{\omega})$. The results indicate a crossover in the short-time short-distance dynamics at low $U$ characterized by ferromagnetic light-cone wavefronts, to a Heisenberg-type behavior at large $U$ featuring antiferromagnetic light cones 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. We discuss experimental candidates for observing the $G(r,t)$ dynamics found at low $U$.