Transport in the XX chain at zero temperature:: Emergence of flat magnetization profiles

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed From -m(0) for x < 0 to m(0) for x > 0. In the long-time limit, the magnetization evolves into a scaling form m(x,t) = Phi(x/t) and the profile develops a flat part (m = Phi = 0) in the \x/t\ less than or equal to c(m(0)) region. The Bat region shrinks to zero if, m(0)-->1/2 while it expands with the maximum velocity c(0) = 1 for m(0)--> 0. The states emerging in the scaling limit an compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems. [S1063-651X(99)03605-3].