One-hole Green function, momentum distribution and quasiparticle weight of the U to infinity 1D Hubbard model

Abstract

Starting from the known Lieb and Wu solution of the one-dimension-Hubbard model in the U to infinity limit, the authors show how the spin-charge decoupling of the elementary excitations is responsible for several peculiar features in one-particle properties, such as momentum distribution, quasiparticle weight and the Green function. In particular they analyse in detail the structure of the one-hole Green function at half-filling, which has not been previously calculated by field theory methods due to the breakdown of conformal invariance. A rich structure is found with branch cut singularities at omega =+or-2 sin k but no simple poles. The non-trivial dependence on the momentum of the hole allows for hole propagation although the analytic structure of G(k, omega ) is quite different from that usually characterizing band insulators. These results provide a precise characterization of one-dimensional Mott insulators. The relationship between the branch cuts of the Green function and the finite-size scaling of the quasiparticle weight is also discussed together with its implications for the analysis of numerical data.