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

• URL: http://arxiv.org/abs/2203.06332v4
• Date: Fri, 5 Aug 2022 19:27:50 GMT
• Title: Magnetic excitations, non-classicality and quantum wake spin dynamics in the Hubbard chain
• Authors: Pontus Laurell and Allen Scheie and D. Alan Tennant and Satoshi Okamoto and Gonzalo Alvarez and Elbio Dagotto
• Abstract summary: Quantum Fisher information (QFI) is a witness of multipartite entanglement, and magnetic Van Hove correlations $G(r,t)$, a probe of local real-space real-time spin dynamics. We show that QFI grows with $U$ and can witness bipartite entanglement above $U=2.5$. We discuss experimental candidates for observing the $G(r,t)$ dynamics found at low $U$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $S(k,\omega)$. 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 $S(k,\omega)$ going from the non-interacting limit ($U=0$) to strong coupling ($U\rightarrow \infty$), where it reduces to the Heisenberg quantum spin chain. We use the density matrix renormalization group (DMRG) to find $S(k,\omega)$, 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 $S(k,\omega)$. The results indicate a crossover in the short-time short-distance dynamics at low $U$ characterized by ferromagnetic lightcone wavefronts, to a Heisenberg-like 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. We discuss experimental candidates for observing the $G(r,t)$ dynamics found at low $U$.

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