C09

Hydrodynamics and gauge/gravity duality for electrons in solids

Summary

This project is devoted to describing dynamical and topological properties of electron systems by adapting concepts and approaches from high-energy physics and quantum field theory. A major role is played by gauge/gravity duality, i.e. generalizations of the AdS/CFT correspondence. A further ingredient is the use of hydrodynamics for analyzing electron flows. For the third funding period we will venture significantly beyond the achievements of the second funding period, in which new results were obtained in particular for electron hydrodynamics at both strong and weak coupling, for the impact of quantum anomalies, and for Kondo systems. The central goals are to obtain new predictions for electron flows and for strongly correlated systems. To this effect, we will focus on five objectives: (1) Study of the implications of special flow geometries and of turbulence for electronic fluid flows, in particular in strongly correlated Kagome metals; (2) Development of a comprehensive formalism for spin hydrodynamics and its application to graphene and to HgTe; (3) Understanding the emergence of zeroes in single-particle Greens functions in strongly interacting Mott insulators; (4) Obtaining new predictions for PT symmetric strongly correlated phases from AdS/CFT, (5) Establishing discrete holographic dualities between hyperbolic lattices and spin chains.