Strong zero modes in a class of generalised Ising spin ladders with plaquette interactions

We study a class of spin-$1/2$ quantum ladder models with generalised plaquette interactions in the presence of a transverse field. We show that in certain parameter regimes these models have strong zero modes responsible for the long relaxation times of edge spins. By exploiting an infinite set of symmetries in these systems, we show how their Hamiltonians can be represented, in each symmetry sector, by a transverse field Ising chain. Due to the presence of an extensive number of conserved quantities, even if the original system has no disorder, most of these symmetry sectors feature a quasi-random transverse field profile. This representation of the ladder system in terms of a disordered Ising chain allows to explain the features of the edge autocorrelation function of the original system.