Disorder-induced two-body localized state in interacting quantum walks

We observe the onset of nonergodicity from ballistic propagation of a two-body bound state in an interacting discrete-time quantum walk (DTQW) due to time-dependent disorder in the interaction. The effect of the disorder on the two-body state can be interpreted as Anderson-type localization in a projected DTQW, but without saturation of entanglement entropy. We characterize the two-body localization in terms of the rate of growth of entanglement entropy and compute the localization length. We find indications for two distinct growth laws for the entanglement: A logarithmic law in the delocalized phase and a double-logarithmic law in the localized phase. We discuss similarities with many-body localization.