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arXiv:cond-mat/9806125

Comment on the paper ``Bound States in the One-dimensional Hubbard Model''

Fabian H. L. Eßler, Frank Göhmann, V. E. Korepin

Published Jun 9, 1998• 0 citations
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Abstract

We comment on the preprint cond-mat/9805103 by D. Braak and N. Andrei \cite{BrAn98}. We point out that the ``new'' Bethe Ansatz equations presented in \cite{BrAn98} are identical to the Bethe equations for strings introduced by M. Takahashi for the description of thermodynamics in 1972 \cite{Takahashi72}. Some physics suggested in \cite{BrAn98} is incorrect. In particular, all former conclusions made on the basis of the string Bethe equations remain valid.

DOI
10.48550/arxiv.cond-mat/9806125

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We comment on the preprint cond-mat/9805103 by D. Braak and N. Andrei \cite{BrAn98}. We point out that the ``new'' Bethe Ansatz equations presented in \cite{BrAn98} are identical to the Bethe equations for strings introduced by M. Takahashi for the description of thermodynamics in 1972 \cite{Takahashi72}. Some physics suggested in \cite{BrAn98} is incorrect. In particular, all former conclusions made on the basis of the string Bethe equations remain valid.
The ``string'' structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to suggest the validity of thermodynamic Bethe-ansatz equations (TBAE). We furthermore solve TBAE in a strong-coupling expansion series form and obtain the thermodynamic potential which agrees with the known high-temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some additional features of the strongly correlated one-dimensional Hubbard model.
The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model are derived for an attractive on-site interaction of the electrons, extending in this way Takahashi's result for the repulsive Hubbard chain. The results are discussed in several special limits, e.g., interaction much larger than the hopping, U\ensuremath{\rightarrow}0 case, and the high- and low-temperature limits. The dominating states at low temperatures consist of spin-paired electrons (resembling Cooper pairs) and bound states of such pairs. The excitation spectrum and its properties are discussed in the context of superconductivity and resonant valence bonds.