Peter Schmitteckert
Interplay between interaction and disorder in one-dimensional Fermi systems
Supervisor: Prof. U. Eckern [Theoretical physics II]
Date of oral examination: 06/05/1996
114 pages, english
In this work we have presented two methods to study the combined effect of disorder and interaction in one-dimensional Fermi systems. In the first part we have introduced a method to incorporate defects into Bethe ansatz solvable models, and presented rigorous results for the groundstate of a spin-1/2 Heisenberg model with defects. Using the Wiener-Hopf method for solving integral equations we have solved the consistency relations of the algebraic Bethe ansatz in the leading order $1/M$ of the finite size correction in the presence of a magnetic flux $\Phi$ penetrating the ring. In the second part of this work the Density-Matrix Renormalizationgroup (DMRG) method was used to study numerically the influence of potential scatterers onto the phase sensitivity of one-dimensional Fermi systems. It is shown that a single impurity and random disorder reduces the phase sensitivity of one-dimensional Fermi systems. Repulsive interaction enforces this suppression while weak and moderate attractive interactions enhance the phase sensitivity. Increasing the system size enhances the influence of interaction. It turned out that the distribution of the phase sensitivity is log-normal. In addition we have applied the DMRG method to investigate the Friedel oscillations in one dimension. We determined the exponent of the decay for systems containing $M=200$, $500$ sites and interactions ranging from $V$=-1 to 2. Our results are in agreement with an analytical result obtained recently by Wang et al. Summarizing we have presented two methods to study one-dimensional interacting Fermi systems. At first we have constructed integrable models containing defects and calculated analytically groundstate properties. As an alternative approach we extended the DMRG method leading to a powerful numerical tool to study generic impurities. This technique is currently the only available method that one can use to obtain reliable results for the groundstate properties of interacting fermions with disorder for system larger than 30 sites.