Würzburg ToCoTronics Colloquium

Topological quantum chemistry (TQC) framework has provided a complete description of the universal properties of all possible atomic band insulators in all space groups considering the crystalline unitary symmetries. It links the chemical and symmetry structure of a given material with its topological properties. While this formalism filled the gap between the mathematical classi fication and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting
systems. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topology like Kondo or Mott insulators. In this talk I will first introduce TQC and its application to correlated systems.
We will analyze the topology of Kondo using TQC insulators and compare it with many- body results. For Mott insulators I will combine cluster perturbation theory and topological Hamiltonians within TQC. This simple formalism will be applied to calculate to the phase diagram of a representative model. The results are compared to numerically exact calculations from density matrix renormalization group and variational Monte Carlo simulations together with many-body topological invariants.

References

[1] M.G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B.A. Bernevig, Z. Wang , “A complete catalogue of High-Quality Topological Materials “, Nature 566, 480-485 (2019)
[2] B. Bradlyn, L. Elcoro, J. Cano, M.G. Vergniory, Z. Wang, C. Felser, M.I. Aroyo, B.A. Bernevig, “Topological quantum chemistry”, Nature 547 (7663), 298-305 (2017).
[3] All topological bands of all stoichiometric materials, Maia G Vergniory, Benjamin J Wieder, Luis Elcoro, Stuart SP Parkin, Claudia Felser, B Andrei Bernevig, Nicolas Regnault, Science 376 (6595), eabg9094 (2022)
[4] Mikel Iraola, Niclas Heinsdorf, Apoorv Tiwari, Dominik Lessnich, Thomas Mertz, Francesco Ferrari, Mark H Fischer, Stephen M Winter, Frank Pollmann, Titus Neupert, Roser Valenc, Maia G Vergniory,  Physical Review B 104 (19), 195125 (2021)
[5] Dominik Lessnich, Stephen M Winter, Mikel Iraola, Maia G Vergniory, Roser Valenc, Physical Review B 104 (8), 085116 (2021)
[6] Mardna O Soldini, Nikita Astrakhantsev, Mikel Iraola, Apoorv Tiwari, Mark H Fischer, Roser Valenc, Maia G Vergniory, Glenn Wagner, Titus Neupert, arXiv preprint arXiv:2209.10556 (2022)

This talk is also broadcasted via zoom. To enter the meeting, follow the link:
https://uni-wuerzburg.zoom.us/j/63035236463?pwd=U1FXWDJpS3JNajk4cFhoNjRDMSsvUT09