Low-energy theory of thet−t′−t″−UHubbard model at half-filling: Interaction strengths in cuprate superconductors and an effective spin-only description of

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 other 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 ͑cuprate͒ materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second-and third-neighbor hopping parameters, tЈ and tЉ, 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 La 2 CuO 4 . Performing a spin-wave analysis, we calculate the magnon dispersion as a function of U, t, tЈ, and tЉ. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. ͓Phys. Rev. Lett. 86, 5377 ͑2001͔͒ for La 2 CuO 4 . The ring exchange terms are found essential, in particular to determine the relative sign of tЈ and tЉ, 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 ͑1999͔͒. We find a value of the interaction strength U Ӎ 8t consistent with Mott insulating behavior.

Collinear antiferromagnetic state in a two-dimensional Hubbard model at half filling

“…Spin frustration can significantly change the magnetic excitations in the antiferromagnetic state. 19 Beyond half filling, ferromagnetic state, incommensurate spin-density-wave state, and phase separation 20 between these states can also appear.…”

Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering

“…With hole doping the trend observed in RIXS is fully recovered only in the Hubbard model, as shown in Fig. 2, implying that higher order processes absent in t-J-type models become crucial in quantitatively reproducing the spin wave dispersion 18 .…”

Magnetic susceptibility and simulated neutron signal in the two-dimensional Hubbard model

“…29,39,42 In the case of the insulating high-T c parent compounds, experimental data has primarily been fit using a linear spin-wave theory in the Heisenberg limit at zero temperature. 2,43 This has allowed for a qualitative description of the excitations in terms of spin models and the determination of the strength of the exchange J/t. However, spin models do not describe itinerant fermion systems, such as the doped compounds.…”