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arXiv:cond-mat/0312055 · Physical Review B

Itinerancy effects on spin correlations in one-dimensional Mott insulators

M. J. Bhaseen, Fabian H. L. Eßler, Anja Grage

Published Jan 25, 2005• 16 citations
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Abstract

We consider spin correlations in the one-dimensional (1D) half-filled repulsive Hubbard model. For very large values of the on-site repulsion $U$ the spin correlations are dominated by virtual hopping processes of electrons and are described in terms of a spin-$1∕2$ Heisenberg chain. As $U$ 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 $U$. We comment on the relevance of our results for inelastic neutron-scattering experiments on quasi-1D materials.

DOI
10.1103/physrevb.71.020405

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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 study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U 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 U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U\to \infty and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U\to 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and \eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U=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 study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number D⊥→∞D_{\perp}\to\inftyD⊥​→∞ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping δ=1−nδ=1-nδ=1−n (nnn, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range l⊥l_{\perp}l⊥​. We find that the δδδ-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for δ→0δ\to 0δ→0, provided that there exists a finite range interaction.