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

摘要

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