Spectral Functions dependence on the average density in the Luttinger liquid model

Sammanfattning

The Luttinger liquid model remarkably provides analytical descriptions of one-dimensional materials, where the strongly correlated electron behavior causes the conventional Fermi‑liquid theory to break down. To get experimentally relevant probing of the Luttinger liquid model, this thesis investigates theoretically and numerically how the spectral function depends on the average electron density within the Luttinger band, resulting in spectral features that are accessible through techniques such as angle-resolved photoemission spectroscopy. An extensive overview of the Luttinger model is presented, culminating in analytical expressions for the spectral function that permit numerical evaluation. Lithium molybdenum purple bronze serves as a central experimental relevant example. The analysis reveals that the g‑ology coupling parameters are effectively independent of density due to screening. Reducing the density dependence of the spectral function primarily to that of the Fermi velocity. In Lithium molybdenum purple bronze specifically, the charge and spin density wave velocities closely track the Fermi velocity and the spectral exponent remains close to zero. These results identify concrete experimental signatures within the spectral function that can be used to detect and characterize one-dimensional Luttinger liquid behavior.