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arXiv:cond-mat/9808018 · Physical review. B, Condensed matter

Form factors in the half-filled Hubbard model

Fabian H. L. Eßler, V. E. Korepin

Published Jan 15, 1999• 8 citations
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Abstract

We consider dynamical spin-spin correlation functions in the one-dimensional repulsive half-filled Hubbard model. We propose an exact expression for the two-spinon form factor of spin operators. We use this to derive the two-spinon contribution to the dynamical structure factor.
DOI
10.1103/physrevb.59.1734

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We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion UUU at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of UUU is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$ and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit $U\ensuremath{\rightarrow}0$. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and $\ensuremath{\eta}$-spin SU(2)\text{SU}(2)SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U=0U=0U=0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.
We consider spin correlations in the one-dimensional (1D) half-filled repulsive Hubbard model. For very large values of the on-site repulsion UUU the spin correlations are dominated by virtual hopping processes of electrons and are described in terms of a spin-1∕21∕21∕2 Heisenberg chain. As UUU is decreased real hopping processes of electrons become important and eventually dominate the spin response. We discuss the evolution of the dynamical structure factor as a function of UUU. We comment on the relevance of our results for inelastic neutron-scattering experiments on quasi-1D materials.