Non-ergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain

We investigate the one-magnon dynamics of the antiferromagnetic delta chain as a paradigmatic example of tunable equilibration. Depending on the ratio of nearest and next-nearest exchange interactions the spin system exhibits a flat band in one-magnon space - in this case equilibration happens only partially, whereas it appears to be complete with dispersive bands as generally expected for generic Hamiltonians. We provide analytical as well as numerical insight into the phenomenon.