Long coherence times for edge spins

TL;DR

This paper demonstrates that edge spins in certain one-dimensional chains maintain their initial state for extremely long times due to strong zero modes, even at high temperatures and with weak perturbations.

Contribution

It introduces the concept of an 'almost' strong zero mode in perturbed chains, explaining prolonged coherence times without disorder.

Findings

Edge spins retain memory for very long times in ordered chains.

Strong zero modes lead to infinite coherence times in integrable models.

Perturbed chains exhibit exponentially long coherence times due to almost strong zero modes.

Abstract

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.