J. Stein: Flow equations and the strong-coupling expansion for the Hubbard model, J. Stat. Phys. 88 (1997) 487 (Postscript-File)
Applying the method of continuous unitary transformations to a class of Hubbard models, the derivation of the t/U-expansion for the strong-coupling case is re-examined. 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 of t/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 order t^3/U^2 or higher.