Interacting one-dimensional systems
One-dimensional quantum systems have the extraordinary property that their low-energy degrees of freedom can be described (almost) exactly, even in the presence of interactions, using
the framework of bosonization and Luttinger liquid theory. This theory allows the calculation of thermodynamic properties and correlation functions, and its predictions have been verified
in numerous experiments.
The only approximation within Luttinger liquid theory is the assumption that the single-particle spectrum is strictly linear. In contrast, non-linearities of the spectrum lead to corrections which become increasingly important at higher energies, and which make an exact solution impossible.
As important examples, such non-linearities lead to notable modifications of the dynamic correlation functions and also introduce qualitatively new effects, like relaxation and thermalization, which are entirely absent in Luttinger liquid theory. We study those effects which require extending Luttinger liquid theory in various directions.
Recently, we have focused in particular on one-dimensional systems with Rashba spin-orbit coupling, which is present for instance in indium arsenide or indium antimonide quantum wires. When coupled to superconductors, these wires have become an important resource for engineering topological states, such as Majorana bound states or parafermionic states which could have important applications in quantum computing.