Interacting Topological Phases in Condensed Matter
Topological states, examples of exotic quantum matter, are intrinsically immune to disorder and have promising applications to dissipationless transport in electronics and spintronics. On the other hand, electron correlation in solids gives rise to a wide variety of collective phenomena, and can play a complicated role in topological states. The interplay of topological and conventional order is subtle and challenges our understanding of quantum many-body behavior in real materials.
For situations where topology and strong correlations are relevant, numerical simulations are essential. In this talk, I will introduce one of the topological states: topological insulators. Topological insulators are a type of quantum matter, with an insulating bulk but time-reversal symmetry protected gapless edge (or surface) states. I will describe two numerical approaches: quantum Monte Carlo methods (QMC) and dynamical mean-field theory, both of which have been shown to be useful to study strongly correlated systems. I will show how correlation influences the topological states using the QMC method. We have found that symmetry may play an essential role for a correlated topological insulator.
Finally, I will introduce another exotic topological state, Weyl semimetals, which have bulk gapless excitations and are driven by electron correlations in pyrochlore iridates. Several perspectives on the correlated topological phases are proposed.