Magnetic excitations, non-classicality 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 $S(k,\omega )$. 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 ($U\to \infty$), 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 $U$.

15 pages, 10 figures

References in corpus (15)

• Entanglement detection
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Spectral Functions with the Density Matrix Renormalization Group: Krylov-space Approach for Correction Vectors
• Witnessing entanglement in quantum magnets using neutron scattering
• Multipartite entanglement detection via structure factors
• Quantifying and controlling entanglement in the quantum magnet Cs${}_2$CoCl${}_4$
• Experimental realisation of multipartite entanglement via quantum Fisher information in a uniform antiferromagnetic quantum spin chain
• Generalized Spectral Signatures of Electron Fractionalization in Quasi-One and -Two Dimensional Molybdenum Bronzes and Superconducting Cuprates
• Quantum spin correlations in an organometallic alternating sign chain
• Spin and charge dynamics of the one-dimensional extended Hubbard model
• Entanglement entropy and entanglement witnesses in models of strongly interacting low-dimensional fermions
• Photoemission Spectroscopy and the Unusually Robust One Dimensional Physics of Lithium Purple Bronze
• Unveiling quantum entanglement in many-body systems from partial information
• Magnetic excitation spectra of strongly correlated quasi-one dimensional systems: Heisenberg versus Hubbard-like behavior

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