Green function and excitation of a singular oscillator

V. V. Dodonov, E.V. Kurmyshev, Vladimir I. Man’ko

Alberto Parola, Sandro Sorella

An exact expression for the Green's function G(k,\ensuremath{\omega}) of one hole in the U\ensuremath{\rightarrow}\ensuremath{\infty} one-dimensional Hubbard model is derived from the known Bethe-ansatz solution of the model. Due to the spin-charge decoupling of the one-hole excitation spectrum and the Fermi-like statistics of the spin excitations, G shows branch-cut singularities at \ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}2 sink and a nontrivial dependence on the momentum of the hole. As a result, the hole can propagate although the quasiparticle weight vanishes.

Fabian H. L. Eßler

We consider excitations with the quantum numbers of a hole in the one-dimensional Hubbard model below half-filling. We calculate the finite-size corrections to the energy. The results are then used to determine threshold singularities in the single-particle Green's function for commensurate fillings. We present the analogous results for the Yang-Gaudin model (electron gas with $\ensuremath{\delta}$-function interactions).

V. V. Dodonov

BERTRAND G. GIRAUD

A mean field approximation allows microscopic calculations of an N-body propagator G(z) = (z − H)-1. We investigate singularities of the resulting approximate Green's function, Gmf(z), by comparing them to the binding energies calculated by the Hartree-Fock approximation. We show that each Hartree-Fock energy induces a singularity of Gmf.

Dušan Popov