Antal T, Krapivsky P L, Rákos A
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 1):061115. doi: 10.1103/PhysRevE.78.061115. Epub 2008 Dec 16.
We study zero-temperature quantum spin chains, which are characterized by a nonvanishing current. For the XX model starting from the initial state mid R:cdots, three dots, centered upward arrow upward arrow upward arrow downward arrow downward arrow downward arrowcdots, three dots, centered 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 subleading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.
