Speaker
Description
Abstract
Kramers–Wannier duality is one of the central ideas in statistical mechanics, relating the high- and low-temperature phases of the Ising model and leading to the exact determination of the critical point. In recent years, it has also emerged as a prototype of a non-invertible symmetry.
In this talk we revisit the duality of the quantum Ising chain from a modern perspective, showing how the Kramers–Wannier transformation can be interpreted as a non-invertible “half-step” translation symmetry. We then connect this picture with the conformal blocks and fusion rules of the critical Ising conformal field theory, leading to a fractionalized description of the Ising spin degrees of freedom. These ideas reveal deep links between generalized symmetries, anyons, conformal field theory and tensor-network wave functions