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

TL;DR

This study uses the Hubbard model and advanced numerical methods to analyze high-energy spin spectral weight in La$_2$CuO$_4$, revealing intermediate coupling regimes, limitations of spin-wave theory, and evidence for d-wave spinon pairing.

Contribution

It introduces a combined numerical and theoretical approach to accurately describe high-energy spin excitations and suggests ground-state d-wave spinon pairing in the Hubbard model for La$_2$CuO$_4$.

Findings

Spectral weight extends up to 566 meV near [π,π]

Intermediate U/8t ratio (~0.76) fits experimental data

Linear spin-wave theory is inadequate for high-energy excitations

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 $[\pi,\pi]$.