  We show that in certain one-dimensional spin chains with open boundary
conditions, the edge spins retain memory of their initial state for very long
times. The long coherence times do not require disorder, only an ordered phase.
In the integrable Ising and XYZ chains, the presence of a strong zero mode
means the coherence time is infinite, even at infinite temperature. When Ising
is perturbed by interactions breaking the integrability, the coherence time
remains exponentially long in the perturbing couplings. We show that this is a
consequence of an edge "almost" strong zero mode that almost commutes with the
Hamiltonian. We compute this operator explicitly, allowing us to estimate
accurately the plateau value of edge spin autocorrelator.
