Topological order from strong correlations

• Applicant: Dr. Maria Hermanns
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 264273015

Ever since the discovery of the fascinating properties of the fractional quantum Hall liquids - the exact quantization of the Hall conductivity, the presence of protected edge states and the enigmatic phenomena of fractional charge and anyonic statistics - the study of topologically ordered phases of matter has been a central endeavor in theoretical condensed matter physics. The last few years have seen a surge of interest driven by new experiments that show that many more real systems might in fact be topologically ordered than was thought earlier. Of special significance has been the discovery of the topological insulators. In this project we will investigate how topological order emerges from strong correlations. In particular, we want to gain a deeper understanding of what types of topological order that can be realized in actual materials under specific experimental conditions, and what are their properties. Detecting and characterizing topological order requires newly developed diagnostic tools, such as various measures of entanglement. An important part of the proposed project is to gain a deeper understanding of these tools, to improve them and to develop new ones. We focus our analysis on two kinds of system, where topological order occurs prominently - quantum Hall and spin liquids. Quantum Hall liquids show a rich variety of topological phases, among them phases that support non-Abelian quasiparticle excitations. We want to improve the understanding of the mechanisms behind the emergence of these phases and what types of topological order that can be stabilized. In order to study these systems, we will use existing diagnostic tools (both analytical and numerical), as well as develop new ones. Within the field of frustrated magnetism, a new, unexplored, research direction has emerged due to the recent discovery of exactly solvable, three-dimensional models that harbor spin liquid phases. We will determine what kind of spin liquids can be stabilized in such models, determine their properties, and look for possible experimental realizations. Instabilities of these spin liquid phases may drive the system into new and interesting topological phases. Our analysis will not only improve our understanding of quantum Hall and spin liquids, but of topologically ordered phases in general.

• DFG Programme: Independent Junior Research Groups