Abstract
The Harper model describes a 1D lattice with a periodic potential. For an irrational potential period, the model exhibits strong-weak duality and localization transitions. This model is a 1D reduction of the Hofstadter model on a square lattice, where the potential period corresponds to the magnetic flux, and the duality comes from a lattice rotation.
Most studies focus on the square lattice. For more general space groups, do similar 1D Harper-type models exist? This talk presents our research plan.
People have already developed a criterion to decide whether a space group can retain its symmetry under a uniform magnetic field. Using this criterion, we plan to:
· Identify space groups that meet the symmetry condition;
· Construct lattice models for these groups and derive 1D Harper-like models;
· Study parameter dualities and possible new phase transitions.
We expect that more complex space groups will lead to richer duality and localization behavior. This talk will cover the criterion, the models we plan to build, and expected outcomes.
Anyone interested is welcome to attend.