10 December 2024 Tue 4 pm

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 Z4 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 Z4 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 Z4 symmetry

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