Mendoza-Arenas J J, Clark S R, Jaksch D
Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042129. doi: 10.1103/PhysRevE.91.042129. Epub 2015 Apr 23.
In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit. We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently, we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.
在这项工作中，我们分析了由于可积性破缺，非平衡一维量子系统中扩散能量传输和局部热化的同时出现。具体而言，我们讨论了具有交错磁场的XXZ自旋链中热边界驱动所诱导的稳态的局部性质。通过对系统运动方程进行高效的大规模矩阵积模拟，我们计算了其在长时间极限下的稳态。我们首先讨论系统所支持的能量传输，发现在可积极限下它是弹道式的，而当交错场有限时则是扩散式的。随后，我们研究了相邻格点的约化密度算符，发现对于大系统，即使在弱交错场的情况下，它们在不可积区域也能很好地由基础哈密顿量的局部热态近似。另一方面，在可积极限下，这种行为消失，并且不再能够确定局部温度。我们的结果与能量扩散和热化之间的直观联系相符。
