Duality defects in two-dimensional statistical mechanics on the lattice

We explore applications of topological defect lines in 2D statistical mechanics models on and off the critical point. In particular, we discuss an extension of Kramers-Wannier duality. The duality is implemented by a topological defect line that separates the model from its dual. Away from criticality, we explain how duality defects make it possible to find non-topological defects that localize a topological degree of freedom. In certain cases, this degree of freedom appears in the quantum spin chains as a zero mode. We will elucidate these results with a variety of concrete examples including the Ising, Fibonacci and super-symmetric models.