I will report on our theoretical investigations of an interface in the transverse field quantum Ising chain connecting an ordered ferromagnetic phase and a disordered paramagnetic phase that are Kramers-Wannier duals of each other. Unlike prior studies focused on non-invertible defects, this interface exhibits a symmetry that combines Kramers-Wannier transformation with spatial reflection. We demonstrated that, under open boundary conditions, this setup gives rise to a discrete Z_4 symmetry, encompassing the conventional Ising parity as a subgroup, while in a closed geometry a non-invertible symmetry emerges. Using the Jordan-Wigner transformation, we maped the spin chain onto a solvable quadratic Majorana fermion system. In this formulation, we constructed Majorana strong zero modes that retain the Z_4 symmetry, ensure degeneracies of all energy eigenstates, and are robust under generic local symmetry-preserving perturbations of the fermion model, including interactions. In an open geometry of the studied model, we identified two regimes that exhibit different degeneracy patterns. I will discuss whether this is a manifestation of distinct fermion symmetry-protected topological orders protected by the Z_4 symmetry.
Zoom link: https://icts-res-in.zoom.us/j/93394092259?pwd=67cILGsDHzXKaWwXfu34rtDBayPnnT.1
Meeting ID: 933 9409 2259
Passcode: 292930