Shift-invert diagonalization of large many-body localizing spin chains
Shift-invert diagonalization of large many-body localizing spin chains
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DOI：
10.21468/scipostphys.5.5.045
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发表时间：
2018-03
期刊：
影响因子：
5.5
通讯作者：
Francesca Pietracaprina;Nicolas Macé;D. J. Luitz;F. Alet
中科院分区：
文献类型：
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作者：
Francesca Pietracaprina;Nicolas Macé;D. J. Luitz;F. Alet
我们提供了一个教学回顾的计算高激发态的无序相互作用量子系统可以经历多体局域化（MBL）跃迁，使用移位逆精确对角化。我们还在https://bitbucket.org/dluitz/sinvert_mbl上提供了一个示例代码。通过对随机场海森堡自旋链模拟参数的详细分析，为如何进行有效的计算提供了实用的指导。我们给出了尺寸为L=26L=26的自旋链的中谱本征态数据。这项工作也面向对并行稀疏线性代数技术的效率感兴趣的读者，这些技术将在MBL问题中找到具有挑战性的应用。
We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to L=26L=26. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem.