Narrow-Band Expansions in the Hubbard Model: A Comment

The connection between a solution of the Hubbard Hamiltonian obtained by Esterling and Lange and the low-density solution is discussed. It is shown that their solution agrees to first order in the bandwidth with the exact solution for the two-electron $N$-site case. However, even this correct first-order expansion fails to adequately account for the low-frequency behavior of the Green's function and related quantities.