Couple exchanges vows among sandbags, flood waters

While many families in western Iowa are busy trying to protect their homes from rising flood waters one couple refused to let anything, even a natural disaster, get in the way of their wedding day.

Cacie and Travis Krampers started planning their big day months ago. The ongoing flooding was not part of the plan.

They took a light-hearted approach to the piles and piles of sandbags outside of the Hilton Garden Inn where the ceremony was held and went ahead with their exchange vows.

This is perhaps a good place to note that on a lattice the distinction between having a net magnetic field and not having it at all is not as sharp as it may seem. Essentially, it is always possible to stick a full flux quantum through some subset of loops on the lattice to shift the average magnetic field without affecting the actual physics. From this perspective, the physics in these flat-band models has a family resemblance to earlier studies of lattice versions of the FQHE [7, 8] with uniform magnetic fields. In this earlier work, the authors studied a fixed filling factor while varying the flux per plaquette from small values and large unit cells, where the standard Landau level description holds, to somewhat larger flux values and smaller unit cells, where that description broke down. As they were able to change this parameter without any evidence of encountering a phase transition, the latter limit constituted an observation of the FQHE in the presence of strong lattice effects. Needless to say, a more analytic approach can be expected to clarify this possible equivalence between this earlier “Hofstadter” and the current “Haldane” versions of the FQHE.

The present work also leaves open several other interesting questions: Can analytic expressions for the wave functions for the ground states and elementary excitations of the FQHE in the lattice models be found, and can they be related to those for the continuum FQHE? Can these FQHE states be realized in materials via this route at high temperatures, as speculated by Tang et al. [1]? Further afield, while an experimental example of a Chern insulator (an insulator with filled bands with a nonzero net Chern number, such as the Haldane model) has yet to be found, at least one example of the related two-dimensional topological insulators with time-reversal symmetry has been found. The band structures in such topological insulators also have nontrivial topology and can even be understood in terms of Chern numbers in certain cases. This raises the possibility that a time-reversal-symmetric version of the FQHE may arise in such models when interactions are added, and may be more readily observable. More ambitiously, it invites the conjecture that three-dimensional “strong” topological insulators, whose band topology is now qualitatively different from that denoted by the Chern numbers that are the focus of attention in this current work, might also give rise to fractional analogs by the same mechanism of including interactions in flattened bands with nontrivial topology.