| Abstract: | A surprising theoretical insight of the last years has been that band insulators of non-interacting fermions, once presumed to be the most boring states of matter, actually come in a topological variety resulting in phenomena like protected metallic surface states and Majorana fermions. In a parallel advance, trapping of ultra-cold atoms in optical lattices has allowed to observe insulating states of bosons rather than fermions. Bosons unlike fermions require interactions to prevent them from condensing, making Bose insulators inherently more complex than their fermionic counterparts. Can they harbor hidden structure analogous to topological band insulators of Fermions? I will show that bosons at integer filling in a one dimensional lattice can indeed form two gapped phases that differ only by topology. The structure of the ground states gives rise to fascinating phenomena, including hidden order and edge states that carry a fractional charge. Surprisingly these "insulators" in fact allow dissipationless transport of quantized charges by topological pumping protocols. I will discuss an extension of these ideas to higher dimensional Bose systems as well as possible realizations with ultra-cold atoms. |
