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

T. Antal·Z. Rácz·A. Rákos·G. M. Schütz
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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)=P(x/t) and the profile develops a flat part (m=P=0) in the |x/t|< 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.

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T. Antal, Z. Rácz, A. Rákos, G. M. Schütz. 1998-12-15. Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles. https://doi.org/10.1103/physreve.59.4912

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