Anyonic self-induced disorder in a stabilizer code: quasi-many body localization in a translational invariant model

Understand

We enquire into the quasi-many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors.

• Our study verifies that random arrangement of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such multi-component anyonic liquid.
• This non-ergodic dynamic suggests a promising scenario for investigation of quasi-many-body localization.
• Computing standard diagnostics evidences that, in such disorder-free many-body system, a typical initial inhomogeneity of anyons gives birth to a glassy dynamics with an exponentially diverging time scale of the full relaxation.