Equality of magnetization and edge current for interacting lattice fermions at positive temperature

In this talk we study interacting fermions on a discrete finite lattice subject to a homogeneous magnetic field at positive temperature. One prime example of such systems is the Hofstadter-Hubbard model. We show that the magnetization is equal to the edge current in the thermodynamic limit if the system satisfies local indistinguishability of the Gibbs state. This latter assumption is known to hold for sufficiently high temperatures. The result implies that the edge currents in such systems are determined by bulk properties and are stable against perturbations near the boundaries.
The talk is based on doi.org/10.1007/s11040-024-09495-8.