Topologische Ordnung durch starke Korrelationen
Zusammenfassung der Projektergebnisse
The project was divided between two of the most prominent areas of topologically ordered phases - the fractional quantum Hall effect and a particular type of quantum spin liquids, namely Kitaev spin liquids. In the fractional quantum Hall effect, we studied an interesting series of non-abelian quantum Hall states. We were able to determine their topological order for the full series and even identify the underlying conformal field theory description for a subset. The latter is conjectured to make certain properties manifest. In particular, it makes it possible to read off the braiding matrices of the emergent quasiparticles, which is essential information for any practical purpose. The underlying conformal field theory allows us to write the wave functions of the ground and excited states as matrix product states and thus verify their (conjectured) properties numerically. The numerical implementation is, however, still work in progress. We have made a considerable progress in this direction by determining the matrix product state structure of the so-called composite fermion states, and are currently optimizing our numerical code. Regarding the Kitaev spin liquids, we were able to comprehensively classify the possible spin liquid states using realistic lattice structures and their underlying symmetries. While this was not part of the original proposal, it proved to be an essential starting point for various important research directions. It allowed us to conduct our study of chiral spin liquids and entanglement properties in a far more systematic manner. It also made it possible to study experimental signatures of Kitaev spin liquids in great generality. While the research within this project was focused on the zero-temperature properties of Kitaev spin liquids, real comparison with experiments forces us to thoroughly understand the finite-temperature properties. This study was beyond the original project description as it necessitates sophisticated numerical efforts. However, several follow-up works were conducted in a collaborative effort to classify thermodynamic properties of Kitaev spin liquids in general, determine the role of geometric frustration on the gauge sector, and identify the effects of finite-temperature on bond-energy correlations - correlation functions that can be measured experimentally and are capable of distinguishing the different spin liquid phases unambiguously.
Projektbezogene Publikationen (Auswahl)
- Classification of gapless Z2 spin liquids in three-dimensional Kitaev models, Phys. Rev. B 93, 085101 (2016)
Kevin O’Brien, Maria Hermanns, Simon Trebst
(Siehe online unter https://doi.org/10.1103/PhysRevB.93.085101) - Conformal field theory construction for nonabelian hierarchy wave functions, Phys. Rev. B 96, 245107 (2017)
Yoran Tournois and Maria Hermanns
(Siehe online unter https://doi.org/10.1103/PhysRevB.96.245107) - Crystalline Kitaev spin liquids, Phys. Rev. B 96, 155107 (2017)
Masahiko G. Yamada, Vatsal Dwivedi, and Maria Hermanns
(Siehe online unter https://doi.org/10.1103/PhysRevB.96.155107) - Entanglement in 3D Kitaev Spin Liquids, J. Stat. Mech. (2018) 063101
Stephanie Matern and Maria Hermanns
(Siehe online unter https://doi.org/10.1088/1742-5468/aac12c)
