We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.

arXiv:cond-mat/9903008Physical review. B, Condensed matterSep 15, 199916 citations

Journal of Mathematical Sciences

Correlators of densities in the one-dimensional hubbard model

N. I. Abarenkova, Anatoli G. Izergin, A. G. Pronko

Published Oct 1, 2000• 4 citations

Publisher

DOI: 10.1007/bf02680139

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V

in the one-dimensional extended Hubbard chain has been examined recently, its effect in the Hubbard model beyond the one-dimensional chain remains unclear. Here, we report a density matrix renormalization group study of the extended Hubbard model on long four-leg cylinders on the square lattice. We find that the near-neighbor electron attraction

V

can notably enhance the long-distance superconducting correlations while simultaneously suppressing the charge-density-wave (CDW) correlations. Specifically, for a modestly strong electron attraction, the superconducting correlations become dominant over the CDW correlations with a Luttinger exponent ${K}_{sc}\ensuremath{\sim}1$ and strong divergent superconducting susceptibility. Our results provide a promising way to realize long-range superconductivity in the doped Hubbard model. The relevance of our numerical results to cuprate materials is also discussed.

We calculate

2{k}_{F}

and

4{k}_{F}

charge-density wave (CDW) and spin-density wave (SDW) autocorrelation functions for the one-dimensional Hubbard model using a computer renormalization-group technique previously developed by us. We describe the method and expected accuracy of the results. The correlation functions are calculated for Hubbard parameter

\frac{U}{t}=2,10,50

and for two different band fillings. We obtain, describe, and compare for the first time the magnitudes and temperature dependences of the correlation functions. We find, inter alia, that the

4{k}_{F}

instability arises at very large

U

and that the

2{k}_{F}

SDW and

4{k}_{F}

CDW dominate at large

U