Transport in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XX</mml:mi></mml:math>chain at zero temperature: Emergence of flat magnetization profiles

Abstract

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)<or=c(m(0)) region. The flat 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 are 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.