Numerical Investigation of Spin Excitations in a Doped Spin Chain

Abstract

We study the doping evolution of spin excitations in a 1D Hubbard model and its downfolded spin Hamiltonians, by using exact diagonalization combined with cluster perturbation theory. In all models, we observe hardening (softening) of spin excitations upon electron (hole) doping, which are reminiscent of recent experiments on 2D cuprate materials. We also find that the 3-site and even higher-order terms are crucial for the low-energy effective spin models to reproduce the magnetic spectra of doped Hubbard systems at a quantitative level. To interpret the numerical results, we further employ a strong coupling slave-boson mean-field theory. The mean-field theory provides an intuitive understanding of the overall compact support of dynamic spin structure factors, including the shift of zero-energy modes and change of spin excitation bandwidth with doping. Our results can serve as predictive benchmarks for future inelastic x-ray or neutron scattering experiments on doped 1D antiferromagnetic Mott insulators.

12 pages, 6 figures

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• Ground state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model
• Unravelling the Nature of Spin Excitations Disentangled from Charge Contributions in a Doped Cuprate Superconductor
• Signatures of the Attractive Interaction in Spin Spectra of One-dimensional Cuprate Chains
• One- and two-particle correlation functions in the cluster perturbation theory for cuprates
• Evolution of the magnetic excitations in electron-doped ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$
• SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order
• Mean Field Study of Superconductivity in the Square Lattice $t$-$J$ Model with Three-Site Hopping
• X-Ray Scattering from Light-Driven Spin Fluctuations in a Doped Mott Insulator