Maia Garcia Vergniory

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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
correlated systems 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 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 HighQuality 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

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Donostia International Physics Center, Donostia-San Sebastian, Spain Ikerbasque, Basque Foundation for Science, Bilbao, Spain
Seminar Room 0.03, ETP
Contact: Sebastian Diehl