Flow equations for Hamiltonians: Crossover from Luttinger to Landau-liquid behaviour in the n-orbital model

Flow equations for Hamiltonians are a novel method for diagonalizing Hamilton operators. They were applied by one of the authors to a one-dimensional SU(n)-symmetric fermionic system, solving the occuring equations to first older of a 1/n-expansion. In this paper, we generalize the procedure to an arbitrary number of spatial dimensions. Although the resulting equations cannot be solved analytically, some information can be extracted about the particle number near the Fermi surface. The results suggest a nonuniversal behaviour for d = 1 which breaks down in favour of that of a Landau liquid in any dimension > 1.