IQ/RQMP : Maia G. Vergniory

Beyond Topological Quantum Chemistry

Maia G. Vergniory
Donostia International Physics Center, Donostia-San Sebastian, Spain
Ikerbasque, Basque Foundation for Science, Bilbao, Spain

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,