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arXiv:cond-mat/9701104 · Physical review. B, Condensed matter

Instabilities of the Hubbard chain in a magnetic field

J. M. P. Carmelo, F. Guinea, Pedro D Sacramento

Published Mar 15, 1997• 19 citations
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Abstract

We find and characterize the instabilities of the repulsive Hubbard chain in a magnetic field by studying all response functions at low frequency \ensuremath{\omega} and arbitrary momentum. The instabilities occur at momenta which are simple combinations of the (U=0) \ensuremath{\sigma}=\ensuremath{\uparrow},\ensuremath{\downarrow} Fermi points, \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$. For finite values of the on-site repulsion U the instabilities occur for single \ensuremath{\sigma} electron added or removed at momenta \ifmmode\pm\else\textpm\fi{}${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\sigma}}}$, for transverse spin-density wave (SDW) at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}}$ (where ${2\mathrm{k}}_{\mathrm{F}}$=${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$+${\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$), and for a charge-density wave and SDW at momenta \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\uparrow}}}$ and \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}\mathrm{\ensuremath{\downarrow}}}$. While removing or adding single electrons is dominant at zero magnetic field, the presence of that field brings about a dominance for the transverse \ifmmode\pm\else\textpm\fi{}${2\mathrm{k}}_{\mathrm{F}}$ SDW over all the remaining instabilities for a large domain of U and density n values. We go beyond conformal-field theory and study divergences which occur at finite frequency in the one-electron Green function at half-filling and in the transverse-spin response function in the fully polarized ferromagnetic phase.

DOI
10.1103/physrevb.55.7565

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Charge-density waves in the Hubbard chain are studied by means of finite-temperature quantum Monte Carlo simulations and Lanczos diagonalizations for the ground state. We present results both for the charge susceptibilities and for the charge structure factor at densities $\ensuremath{\rho}=1/6$ and 1/3; for $\ensuremath{\rho}=1/2$ (quarter filled) we only present results for the charge structure factor. The data are consistent with a 4kF{4k}_{F}4kF​ instability dominating over the 2kF{2k}_{F}2kF​ one, at least for sufficiently large values of the Coulomb repulsion U. This can only be reconciled with the Luttinger liquid analyses if the amplitude of the 2kF{2k}_{F}2kF​ contribution vanishes above some ${U}^{*}(\ensuremath{\rho}).$
We consider fermions on a one-dimensional superlattice, represented by a repeated pattern of repulsive (i.e., positive Hubbard UUU) and free (i.e., U=0U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0U=0) sites. Lanczos diagonalization of chains up to 12 sites at half filling shows that some patterns give rise to a weak form of frustration, sufficient to wipe out the spin-density-wave (SDW) correlations present in the otherwise homogeneous system. On the other hand, SDW correlations appear for some patterns above half filling, a feature absent in the homogeneous case. Below half filling, the local-moment maxima are displaced from the repulsive to the free sites. The peak in the magnetic structure factor is also shifted from $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$, for the alternating configuration when $\ensuremath{\rho}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$ and 5/3.
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