RQMP Research Seminar

Beyond Topological Quantum Chemistry

Maia G. Vergniory

Donostia International Physics Center & Ikerbasque

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 classification 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 strongly correlated system that can exhibit symmetry protected topological Mott insulators. In this talk I will first introduce TQC and its application and then I will address this question by combining cluster perturbation theory and topological Hamiltonians within TQC. This simple formalism will be applied to calculate to the phase diagram of the Hubbard model for a diamond chain. 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] M. Iraola et al, in preparation