2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215225We study zero-temperature quantum spin chains which are characterized by a non-vanishing current. For the XX model starting from the initial state |... + + + - - - ...> we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the sub-leading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.9 pages, 4 figures, minor alterationsStatistical MechanicsStrongly Correlated Electronstext