Flow equations and the strong-coupling expansion for the Hubbard model |
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Authors: | Jürgen Stein |
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Institution: | 1. Institut für Theoretische Physik, Ruprecht-Karls-Universit?t Heidelberg, 69120, Heidelberg, Germany
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Abstract: | Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions
can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of
the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients.
This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and
circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and
it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard
bands can affect the effective Hamiltonian only at ordert
3/U2 or higher. |
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Keywords: | Hubbard model flow equations strong-coupling expansion |
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