Spectral function of one hole in several one-dimensional spin arrangements

The spectral function of one hole in different magnetic states of the one-dimensional t-J model including three-site term and frustration $J^{\mathrm{\prime }}$ is studied. In the strong coupling limit $J\to 0$ (corresponding to $U\to \mathrm{\infty }$ of the Hubbard-model) a set of eigenoperators of the Liouvillian is found which allows to derive an exact expression for the one-particle Green’s function that is also applicable at finite temperature and in an arbitrary magnetic state. The spinon dispersion of the pure t-J model with the ground-state of the Heisenberg model can be obtained by treating the corrections due to a small exchange term by means of the projection method. The spectral function for the special frustration $J^{\mathrm{\prime }}=J\mathrm{/}2$ with the Majumdar-Ghosh wave function is discussed in detail. Besides the projection method, a variational ansatz with the set of eigenoperators of the $t$-term is used. We find a symmetric spinon dispersion around the momentum $k=\pi \mathrm{/}(2a)$ and a strong damping of the holon branch. Below the continuum a bound state is obtained with finite spectral weight and a very small separation from the continuum. Furthermore, the spectral function of the ideal paramagnetic case at a temperature $k_{B}T\gg J$ is discussed.