HLRB Project pr94vu

Numerical simulations of topological and correlated quantum matter

Institut für Theoretische Physik & Astrophysik, Universität Würzburg

Numerical simulations of topological and correlated quantum matter

Institut für Theoretische Physik & Astrophysik, Universität Würzburg

Institut für Theoretische Physik & Astrophysik, Universität Würzburg

Dr. Florian Goth

Am Hubland

97074 Würzburg

Material science corresponds to a multi-scale problem and, as such, hinges on complementary computational methods each adequate in accounting for physics in a given energy window.The aim of this grant proposal is to provide computational resources to three groups at the university of W\"urzburgwho will concentrate on ab-initio calculations, transport, and emergent collective phenomena in materials and models where correlation and/or topological effects play a dominant role.From the methodological point of view, many different codes will be used.This includes state of the art quantum Monte Carlo algorithms for impurity and lattice problems, density functional methods, as well as non-equilibrium Green function techniques.The three groups are members of the DFG-FOR1162 research unit which has given rise to the SFB-1170 initiative in W\"urzburg and which has recently been very positively evaluated.Our common interests lie in systems where inversion symmetry is broken -- as is inevitably the case at surfaces and interfaces -- such that the spin-orbit coupling cannot necessarily be omitted.This coupling between orbital and spin degrees of freedom is a necessary ingredient for the realizatiom of topological insulators.These materials are insulating in the bulk but show robust metallic surface states which are unique in the sense that spin and crystal momentum are tied together.This triggers the possibility of manipulating spin degrees of freedom by coupling to the charge, thereby paving a route to spintronics.Interfaces and surfaces are, per definition, systems with reduced dimensionality. In reduced dimensions electron-electron correlations play a dominant role.One of the main goals of our research is to understand the subtle interplay between correlations and spin orbit coupling.In particular, combined with the electron-phonon interaction, spin-orbit coupling leads to topological superconductivity where vortices can accommodate majorana fermions.Correlation induced topological states of matter, as potentially realized in the heavy fermion compound SmB$_6$, hinge on the subtle interplay of spin-orbit coupling and Coulomb repulsions.More generally, correlations lead to emergent collective phenomena such as magnetism, superconductivity, or more exotic states of matter characterized by fractionalized excitations. The latter includes one dimensional systems, the fractional quantum Hall effect as well as so called spin liquids in two dimensions. Emergent collective phenomena are strictly speaking only well defined upon taking the thermodynamic limit. This confronts us with a huge numerical challenge: taking into account correlation effects between an infinite number of electrons. It is clearly impossible to reach the thermodynamic limit, both experimentally and numerically, but large enough systems will exhibit collective phenomena above an energy scale inversely proportional to the volume of the system.Numerically, this amounts to the importance of being able to carry out simulations on large systems which implies the ability to harness the power of modern supercomputing architectures.

Impressum, Conny Wendler