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

TL;DR

This paper investigates zero-temperature magnetization transport in XX chains, revealing the emergence of flat magnetization profiles and their scaling behavior, with results matching those of homogeneous systems under certain conditions.

Contribution

It introduces a detailed analysis of magnetization dynamics in inhomogeneous XX chains, highlighting the formation of flat profiles and their relation to homogeneous systems.

Findings

Flat magnetization profiles develop in the long-time limit.

The flat region size depends on initial magnetization m_0.

Expectations of physical quantities match between inhomogeneous and homogeneous systems.

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.