Exact single spin flip for the Hubbard model in $d=\infty$

Abstract

It is shown that the dynamics of a single $\downarrow$-electron interacting with a band of $\uparrow$-electrons can be calculated exactly in the limit of infinite dimension. The corresponding Green function is determined as a continued fraction. It is used to investigate the stability of saturated ferromagnetism and the nature of the ground state for two generic non-bipartite infinite dimensional lattices. Non Fermi liquid behavior is found. For certain dopings the $\downarrow$-electron is bound to the $\uparrow$-holes.