Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4

Abstract

Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many new types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band structure calculations and photoemission experiments on these systems, we include second and third neighbor hopping parameters, t' and t'', into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed, four hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4. Performing a spin wave analysis, we calculate the magnon dispersion as a function of U,t,t' and t''. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377, {2001}] for La2CuO4. The ring exchange terms are found essential, in particular to determine the relative sign of t' and t'', with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength U~8t consistent with Mott insulating behavior.

Submitted to Phys. Rev. B, 24 pages, 8 figures, 78 references

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• Superconductivity in high-$T_c$ and related strongly correlated systems from variational perspective: Beyond mean field theory
• Magnetic exchange coupling in cuprate-analog $d^9$ nickelates
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• Collinear antiferromagnetic state in a two-dimensional Hubbard model at half filling
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• Strain-Tuned Magnetic Frustration in a Square Lattice $J_1$-$J_2$ Material
• Magnon interactions in a moderately correlated Mott insulator
• Unravelling the Nature of Spin Excitations Disentangled from Charge Contributions in a Doped Cuprate Superconductor
• Impurity-induced frustration: low-energy model of diluted oxides
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• Suppression of Antiferromagnetism in Electron-Doped Cuprate $T^{\prime }$-${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4\pm \delta }$
• Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model and high-temperature superconductor models
• First principle prediction of structural distortions in the cuprates and their impact on the electronic structure
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Magnon Spectra of Cuprates beyond Spin Wave Theory
• Effect of strain-induced orbital splitting on the magnetic excitations in undoped cuprates
• X-Ray Scattering from Light-Driven Spin Fluctuations in a Doped Mott Insulator
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
• Multimagnon and multispinon $L_3$-edge RIXS spectra of an effective ${\tilde{J}}_1-{\tilde{J}}_2-{\tilde{J}}_3$ square lattice Heisenberg model
• High Harmonic Generation in Two-Dimensional Mott Insulators
• Magnetic Excitations of a Half-Filled Tl-based Cuprate