Dresden 2017 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 61: Correlated Electrons: (General) Theory 2
TT 61.9: Vortrag
Donnerstag, 23. März 2017, 11:45–12:00, HSZ 204
Numerical investigation of the reduction in the topological classification due to interactions in 2D — •Johannes S. Hofmann1, Raquel Queiroz2,3, Eslam Khalaf2, and Fakher F. Assaad1 — 1Institut für Theoretische Physik und Astrophysik, Würzburg, Deutschland — 2Max-Planck-Institut für Festkörperforschung, Stuttgart, Deutschland — 3Weizmann Institute of Science, Rehovot, Israel
Symmetry protected topological phases have been classified for non-interacting models by A. P. Schnyder et. al.[1]. As first shown by Kitaev and Fidkowski[2] for class BDI in 1D and later extended to all symmetry classes [3], interactions lead to a reduction of topologically distinct phases. R. Queiroz et. al. present explicit rules for the construction of such interactions [4].
Here we consider the symmetry class A’ in 2 dimensions, i.e. models with time-reversal, particle-hole and a unitary Z2 symmetry R, where interactions reduce the topological classification from Z to Z4. We realize this class by a lattice Dirac Hamiltonian and the goal of this project is to first confirm the arguments provided in the previous studies numerically by explicitly connecting a topological phase with winding n=4 adiabatically to the trivial insulator (n=0). We then study the mechanism, how both the gap closing and the symmetry breaking, required in the non-interacting model, is avoided.
[1] Schnyder et. al., PRB 78, 195125
[2] Fidkowski and Kitaev, PRB 81, 134509
[3] Morimoto et. el., PRB 92, 125104
[4] Queiroz et. el., PRL 117, 206405