Local and Non-local correlation effects in topological quantum phase transitions

The fate of quantum phase transition among different topological states in presence of strong interaction is of primary interest in condensed matter.
We study the effects of electronic interactions at the local and non-local level in a paradigmatic model for topological insulator in two dimensions.
In the non-interacting regime topological transitions occurs via the continuous closing the energy gap.
Using Dynamical Mean-Field Theory and various cluster extensions (Cluster-DMFT, Variational Cluster Approximation, etc.), we show how short-range correlation effects are responsible for the breakdown of the continuous topological transition in favour of a first-order one. The discontinuous transition occurs without the celebrated closing of the energy gap, yet without the breaking of the symmetries which protect the topological state.

References:
A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, Phys. Rev. Lett. 114, 185701 (2015)
A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni, Phys. Rev. B 93, 235112 (2016)
L. Crippa, A. Amaricci, N. Wagner, G. Sangiovanni, J. C. Budich, and M. Capone,arXiv:1904.11836 (2019)