C09

Hydrodynamics and gauge/gravity duality for strongly correlated electron systems

Summary

This project is the continuation of project C09 that started in November 2017, following a successful ‘Nachantrag’ (Application after the official SFB 1170 start date) by two new PIs who joined Würzburg University in 2016. The central question of this project is the description of dynamical and topological properties of strongly correlated electron systems by adapting concepts and approaches from high energy physics and quantum field theory. A further important ingredient is the use of hydrodynamics. A major role in this context is played by the concept of gauge/gravity duality, i.e. by generalizations of the AdS/CFT correspondence. This correspondence is a duality map between strongly coupled quantum systems and weakly coupled gravitational systems. It has lead to substantial results for the hydrodynamics of strongly correlated systems, and describes strange metallic states of high temperature superconductors. We will use results from gauge/gravity duality together with weak cou- pling approaches to devise observables sensitive to strong coupling behaviour of electrons in solids. The project has three parts. These are related by the use of the methods described above. First, based on our recent results on the Poiseuille flow of strongly correlated electrons in a channel, we will pursue our investigation of hydrodynamics for electrons in solids. We will propose new mea- surements for the ratio of shear viscosity over entropy density and for further coupling-sensitive quan- tities such as the jet-quenching parameter. We will investigate how strongly correlated materials may be realized in which this ratio of shear viscosity over entropy density is close to the AdS/CFT result η/s = 1/(4π). A second topic will be the investigation of further examples of quantum anomalies and their implications for condensed matter systems. In this context we plan to extend recent investiga- tions of a novel hydrodynamic AC response due to the Hall viscosity in 2+1 dimensional systems, as well as of quantum anomalies in superconducting Weyl semimetals. The third part of the project will be devoted to realizing Kondo models within gauge/gravity duality that describe systems of impurities interacting with a strongly coupled electron gas. We will evaluate spectral functions in these models, and make them amenable to experiments, for instance in heavy fermion systems. We will moreover investigate fermionic Hubbard and Kondo lattices within gauge/gravity duality.