Hubbard-model description of the high-energy spin-spectral-weight distribution in La(2)CuO(4)

Abstract

The spectral-weight distribution in recent neutron scattering experiments on the parent compound La${}_2$CuO${}_4$ (LCO), which are limited in energy range to about 450\,meV, is studied in the framework of the Hubbard model on the square lattice with effective nearest-neighbor transfer integral $t$ and on-site repulsion $U$. Our study combines a number of numerical and theoretical approaches, including, in addition to standard treatments, density matrix renormalization group calculations for Hubbard cylinders and a suitable spinon approach for the spin excitations. Our results confirm that the $U/8t$ magnitude suitable to LCO corresponds to intermediate $U$ values smaller than the bandwidth $8t$, which we estimate to be $8t\approx 2.36$ eV for $U/8t\approx 0.76$. This confirms the unsuitability of the conventional linear spin-wave theory. Our theoretical studies provide evidence for the occurrence of ground-state d-wave spinon pairing in the half-filled Hubbard model on the square lattice. This pairing applies only to the rotated-electron spin degrees of freedom, but it could play a role in a possible electron d-wave pairing formation upon hole doping. We find that the higher-energy spin spectral weight extends to about 566 meV and is located at and near the momentum $[\pi ,\pi ]$. The continuum weight energy-integrated intensity vanishes or is extremely small at momentum $[\pi ,0]$. This behavior of this intensity is consistent with that of the spin waves observed in recent high-energy neutron scattering experiments, which are damped at the momentum $[\pi ,0]$. We suggest that future LCO neutron scattering experiments scan the energies between 450 meV and 566 meV and momenta around $[\pi ,\pi ]$.

23 pages, 5 figures

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• Effect of strain-induced orbital splitting on the magnetic excitations in undoped cuprates
• Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/${\mathbb{Z}}_2^2$ symmetry